(-e-x⁢cos(nx)+e-x⁢-sin(nx)⁢n)e-x⁢cos(nx)⁢ln2

(x2(1-2lnx+2)-(x-lnx⁢2x)⁢4x3)x4

cot(π4)π4⁢(sin(π4))ln(π4)

-e-x⁢cos(nx)+e-x⁢-sin(nx)⁢ne-x⁢cos(nx)⁢ln2

x2(1-2lnx+2)-(x-lnx⁢2x)⁢4x3x4

Question 1

Let y=log2(e-x&#8290;cos(nx)). What is dydx?

Accepted Answer

(-e-x&#8290;cos(nx)+e-x&#8290;-sin(nx)&#8290;n)e-x&#8290;cos(nx)&#8290;ln2

Question 2

Given y=lnxx2, what is d2yd2x?

Accepted Answer

(x2(1-2lnx+2)-(x-lnx&#8290;2x)&#8290;4x3)x4

Question 3

Suppose y=(sinx)lnx. What is dydx?

Accepted Answer

cotxx&#8290;(sinx)lnx

Question 4

Let y=ln(e-x&#8290;cos2xx2+x+1). What is dydx?

Accepted Answer

-1+2tanx-2x+1x2+x+1

Question 5

Which of the following best describes the process used to differentiate y=(sinx)lnx?

Accepted Answer

Rewrite using logarithms, then use implicit differentiation and the chain rule.

Question 6

If y=lnxx2, what is dydx?

Accepted Answer

1-2lnxx3

Question 7

Which of the following is the correct application of the chain rule for y=log2(e-x&#8290;cos(nx))?

Accepted Answer

dydx=f'(x)f(x)&#8290;ln2

Question 8

For y=ln(e-x&#8290;cos2xx2+x+1), which of the following is the correct simplification for y?

Accepted Answer

-x+2ln(cosx)-ln(x2+x+1)

Question 9

Which of the following is the correct logarithmic differentiation step for y=(sinx)lnx?

Accepted Answer

lny=lnx&#8290;ln(sinx)

Question 10

If y=(sinx)lnx, what is the value of dydx at x=&#960;4?

Accepted Answer

cot(&#960;4)&#960;4&#8290;(sin(&#960;4))ln(&#960;4)

Question 11

Which of the following is a correct application of the quotient rule for y=lnxx2?

Accepted Answer

x2&#8290;1x-lnx&#8290;2xx4

Question 12

Which of the following is the correct simplification for ln(e-x&#8290;cos2x)?

Accepted Answer

-x+2ln(cosx)

Question 13

If y=(sinx)lnx, which of the following is the correct expression for lny?

Accepted Answer

lny=lnx&#8290;ln(sinx)

Question 14

Which of the following is the correct derivative of y=log2(e-x&#8290;cos(nx)) with respect to x?

Accepted Answer

-e-x&#8290;cos(nx)+e-x&#8290;-sin(nx)&#8290;ne-x&#8290;cos(nx)&#8290;ln2

Question 15

Which of the following is the correct second derivative of y=lnxx2?

Accepted Answer

x2(1-2lnx+2)-(x-lnx&#8290;2x)&#8290;4x3x4

Advanced Differentiation Techniques in Calculus

Study Guide - Practice Questions