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2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021

2.3 Di�erentiation Formulas (Homework)

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2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 2/20

Differentiate the function.

Differentiate the function.

Differentiate the function.

g(t) = 7t + 9t2

g ′(t) =

g(x) = x − 2x + 11 9 4

2

g ′(x) =

V(t) = t + t−3 ⁄ 5 5

V ′(t) =

1. [–/1 Points] SCALC9 2.3.002.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2. [–/1 Points] SCALC9 2.3.004.MI.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

3. [–/1 Points] SCALC9 2.3.008.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHERjavascript:open_bc_enhanced(‘master_it_alt’,%20’/v4cgi/questions/tutorial_popup.tpl?struct=ABAuCsDRDODDEWDLAREtAREXEiCmDtAwBcCbAHADAdBHDnDiCMDUApBfAbDnDUDgEfDnBEDfBwBXCxCxEqAyACDIAcCVCXABCcAhANENEyAQCiDjCOAABjDbAiEXByEDBHBABfDLApEdEyAgEcBhChwWBhBLApAREQBKCcDpBVAgEIAaBgDfEVEGDaEVDXAQDfAwApCICxCqBFDEEFDoAEBqEHCdAMCoAACAERCaEfBnDCCdDFDJCaAPCCDkEyAvDDCWAXAmAgDLEPDnCCEaEmCRDKDCEnDUArETEREACyEgBfAWAPDSDtEWDGDKERDbBFBtCQEfCwADAuEkEqBWBsBKEhAgCwEcEBDWDEADCBAgCLAODDCPAfCIBIDMDwCjEvDSCXBtAyANDvAhDWCKAYBPDGCyuUDw&UserPass=c32844ea290fa05e11c5dedd7a5c8319&current=0&all=0′)

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Differentiate the function.

Differentiate the function.

Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.)

h(w) = w − 6 6

h ′(w) =

S(R) = 9 R2

S'(R) =

F(t) = (5t − 4)2

F ′(t) =

4. [–/1 Points] SCALC9 2.3.012.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

5. [–/1 Points] SCALC9 2.3.014.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

6. [–/1 Points] SCALC9 2.3.016.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHERjavascript:open_bc_enhanced(‘watch_it’,%20’https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalcet6_03_01_013&prod=scalcet6′,%201)javascript:open_bc_enhanced(‘watch_it’,%20’https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalcet8_03_01_015&prod=scalcet8′,%201)

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.)

Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.)

=

y = 7 + 7x

2x

x

2

y ′ =

G(t) = + 6t t

3

G ′(t)

7. [–/1 Points] SCALC9 2.3.018.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

8. [–/1 Points] SCALC9 2.3.020.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules.)

Consider the following.

Find

Find

F(z) = A + Bz + Cz

z

2

2

F ′(z) =

y = + t

x8 x t

. dy dx

=

dy dx

. dy dt

=

dy dt

9. [–/1 Points] SCALC9 2.3.022.DETAILS MY NOTES ASK YOUR TEACHER

10. [–/2 Points] SCALC9 2.3.026.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Find the derivative of the function

in two ways: by using the Quotient Rule and by simplifying first. (Check that your answers are equivalent. Which method do you prefer?)

Quotient Rule =

simplify first =

Use the quotient rule to find the derivative of the function.

F(x) = x − 7x +

x

4 3 x

2

F ′(x)

F ′(x)

G(u) = 5u − 4u u + 1

4

G ′(u) =

11. [–/2 Points] SCALC9 2.3.028.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

12. [–/1 Points] SCALC9 2.3.036.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=27128647 7/20

Differentiate.

Differentiate.

F(x) = 1

3x − 8x + 93 2

F ′(x) =

y = + 7

x

x

y′ =

13. [–/1 Points] SCALC9 2.3.038.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

14. [–/1 Points] SCALC9 2.3.040.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Differentiate.

Differentiate.

Differentiate.

h(w) = (w + 6w )(w − w )5 4 −4 −6

h ′(w) =

F(t) = At

Bt + Ct

2

6 9

F ′(t) =

f(x) = ax + b cx + d

f ‘(x) =

15. [–/1 Points] SCALC9 2.3.046.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

16. [–/1 Points] SCALC9 2.3.050.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

17. [–/1 Points] SCALC9 2.3.052.DETAILS MY NOTES ASK YOUR TEACHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Find an equation of the tangent line to the curve at the given point.

Consider the following.

Find an equation of the tangent line.

y =

Find an equation of the normal line.

y =

y = 3x − x + 6, (2, 26)3 2

y =

y = x , (1, 1)5 ⁄ 4

18. [–/1 Points] SCALC9 2.3.060.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

19. [–/2 Points] SCALC9 2.3.062.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHERjavascript:open_bc_enhanced(‘watch_it’,%20’https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalcet8_03_01_033&prod=scalcet8′,%201)

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Find equations of the tangent line and normal line to the curve at the specified point.

tangent y =

normal y =

y = , 1, 0.2 x + 4

x

20. [–/2 Points] SCALC9 2.3.064.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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A graphing calculator is recommended.

The graph of the function is called a serpentine.

(a) Find an equation of the tangent line to this curve at the point

(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

f(x) = x

1 + x2

(3, 0.30).

y =

21. [–/2 Points] SCALC9 2.3.066.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Find the first and second derivative of the function.

=

=

G(r) = + r r 7

G'(r)

G”(r)

22. [–/2 Points] SCALC9 2.3.068.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHERjavascript:open_bc_enhanced(‘watch_it’,%20’https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?rss=scalccc4_03_02_034&prod=scalccc4′,%201)javascript:open_bc_enhanced(‘watch_it’,%20’https://college.cengage.com/geyser/cengage_9780538738101/html/watchit_player/?asset=scalccc4_03_01_042&prod=scalccc4′,%201)

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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The equation of motion of a particle is where s is in meters and t is in seconds. (Assume t ≥ 0.)

(a) Find the velocity, v(t), and acceleration, a(t), as functions of t.

v(t) =

a(t) =

(b) Find the acceleration (in m/s ) after 1.3 s.

(c) Graph the position, velocity, and acceleration functions on the same screen.

s = t − 4t + t − t,4 3 2

2

a(1.3) = m/s2

23. [–/4 Points] SCALC9 2.3.074.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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The number of tree species S in a given area A in a forest reserve has been modeled by the power function

where A is measured in square meters. Find (Round your answer to five decimal places.)

Interpret your answer.

The rate of change of the number of tree species with respect to area is 0.35599 species/m .

The rate of change of the number of tree species with respect to area is −44.39254 species/m .

The rate of change of the number of tree species with respect to area is −0.35599 species/m .

The rate of change of the number of tree species with respect to area is 44.39254 species/m .

The rate of change of the number of tree species with respect to area is 44.03655 species/m .

Suppose that and Find

(a)

(b)

(c)

(d)

S(A) = 0.882A0.842

S'(105).

S'(105) = species/m2

2

2

2

2

2

f(4) = 4, g(4) = 5, f ′(4) = −3, g ′(4) = 2. h ′(4).

h(x) = 2f(x) + 3g(x)

h ′(4) =

h(x) = f(x)g(x)

h ′(4) =

h(x) = f(x) g(x)

h ′(4) =

h(x) = g(x)

f(x) + g(x)

h ′(4) =

24. [–/2 Points] SCALC9 2.3.076.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

25. [–/4 Points] SCALC9 2.3.080.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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If find

Let and where F and G are the functions whose graphs are shown.

(a) Find

(b) Find

h(2) = 3 and h'(2) = −7,

. d dx

h(x) x

x = 2

P(x) = F(x)G(x) Q(x) = , F(x) G(x)

P'(2).

Q'(7).

26. [–/1 Points] SCALC9 2.3.082.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

27. [–/2 Points] SCALC9 2.3.084.DETAILS MY NOTES ASK YOUR TEACHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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If f is a differentiable function, find an expression for the derivative of each of the following functions.

(a)

(b)

(c)

(d)

y = x f(x)6

y’ = x f ‘(x) + 6x f(x)6 5

y’ = x f ‘(x) − 5x f(x)5 6

y’ = x f(x) − 6x f ‘(x)6 5

y’ = x f(x) + 6x f ‘(x)6 5

y’ = x f ‘(x) + 5x f(x)5 6

y = f(x)

x5

y’ = xf ‘(x) + 4f(x)

x5

y’ = xf(x) + 5f ‘(x)

x5

y’ = xf ‘(x) − 5f(x)

x6

y’ = xf ‘(x) − 4f(x)

x6

y’ = xf(x) − 5f ‘(x)

x4

y = x f(x)

4

y’ = f ‘(x)(3x ) − x f ‘(x)

[f(x)]

3 4

2

y’ = f ‘(x)(4x ) − x f(x)

[f(x)]

3 4

2

y’ = f ‘(x)(3x ) + x f(x)

[f(x)]

4 3

2

y’ = f(x)(3x ) + x f ‘(x)

[f(x)]

4 4

2

y’ = f(x)(4x ) − x f ‘(x)

[f(x)]

3 4

2

y = 7 + xf(x)

x

y’ = xf(x) + 7x f(x) − 2

2x

2

3/2

y’ = xf ‘(x) − 2x f ‘(x) + 7

2x

2

3/2

28. [–/4 Points] SCALC9 2.3.086.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list.)

Find equations of the tangent lines to the curve

that are parallel to the line (Enter your answers as a comma-separated list of equations.)

y’ = xf ‘(x) + 7x f(x) − 2

2x

2

3/2

y’ = xf(x) + 2x f ‘(x) − 7

2x

2

3/2

y’ = xf(x) − 7x f ‘(x) + 7

2x

2

3/2

f(x) = x + 3x + x + 73 2

x =

y = x − 1 x + 1

x − 2y = 5.

29. [–/1 Points] SCALC9 2.3.088.MI.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

30. [–/1 Points] SCALC9 2.3.092.DETAILS

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHERjavascript:open_bc_enhanced(‘master_it_alt’,%20’/v4cgi/questions/tutorial_popup.tpl?struct=AMARDREsBwCPBkBGBjBdAjENCeCrvVCKEPBTABCeDACGCuAvDFCDEJDJBqEQBCEDAWDmDHAUAGErDQBNBvEvChANCSETATwWEjDfEYDoDLArCjBWAqEICUDYCoEhCiEsAwBpyYDlChACAPBXExAJDyDLDxCHApCJEEDABVEmEdCVDoBeClBjAIDsCsCnBQzZEABNCABoEDDsCTBlBXDEDDCyAwCOAsBmDDCDDrCtEOEMDTCmETEyAqCMBVCHEQEsAOBoAkDmCdCgAaDkEEAvBUCgBnBkBtEFDOASCADPDfvVDLDsCdDYEeAtATDUCRBcEoAmCMAWyYEgAWAADNCXAvESCvEUEoDgAnEjAeCmCPAcAYDyEgERDmEHCKAhDJEfAEENCwEGDvzUBtEABxCsCiAuCXCDBNEl&UserPass=c32844ea290fa05e11c5dedd7a5c8319&current=0&all=0′)

2021/9/18 下午10:05 2.3 Differentiation Formulas – Fal21 MATH 005A #71943 SINGLE VARIABLE CALCULUS I, Fall 2021 | WebAssign

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Find equations of both lines through the point (2, −3) that are tangent to the parabola

smaller slope y =

larger slope y =

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y = x + x.2

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31. [–/2 Points] SCALC9 2.3.096.DETAILS MY NOTES ASK YOUR TEACHERhttps://www.cengage.com/legal/#termshttps://www.cengage.com/privacy/

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