e-xcos(nx)⋅ln2⋅(-e-xcos(nx)+e-x-sin(nx)n)

Question 1

Given y=log2(e-x&#x22C5;cos(nx)), which of the following is the correct expression for dydx?

Accepted Answer

e-xcos(nx)&#x22C5;ln2&#x22C5;(-e-xcos(nx)+e-x-sin(nx)n)

Question 2

For y=lnx, what is the correct expression for y&#x2032;&#x2032; (the second derivative)?

Accepted Answer

x2-lnx&#x22C5;2xx3

Question 3

Given y=(sinx)lnx, which of the following is the correct derivative dydx?

Accepted Answer

cotx&#x22C5;(sinx)lnx+lnx

Question 4

For y=(sinx)lnx, which logarithmic property is used to rewrite ln((sinx)lnx)?

Accepted Answer

Power rule for logarithms

Question 5

Given y=ln(e-x&#x22C5;cos2xx2+x+1, which of the following is the correct first derivative?

Accepted Answer

2x+1x2+x+1-2tanx-1+e-xcos2xx2+x+1

Question 6

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

Accepted Answer

Logarithmic differentiation

Question 7

If y=lnx, what is the value of dydx at x=1?

Accepted Answer

0

Question 8

Which of the following is the correct simplification for ln(e-x&#x22C5;cos2x)?

Accepted Answer

-x+2ln(cosx)

Question 9

Suppose y=(sinx)lnx. Which of the following is the correct expression for dydx?

Accepted Answer

cotx&#x22C5;(sinx)lnx+lnx

Question 10

Which rule is most appropriate for differentiating y=(sinx)lnx?

Accepted Answer

Logarithmic differentiation

Question 11

If y=lnx, what is the value of dydx at x=1?

Accepted Answer

0

Question 12

Which of the following is the correct simplification for ln(e-x&#x22C5;cos2x)?

Accepted Answer

-x+2ln(cosx)

Question 13

Suppose y=(sinx)lnx. Which of the following is the correct expression for dydx?

Accepted Answer

cotx&#x22C5;(sinx)lnx+lnx

Question 14

Which rule is most appropriate for differentiating y=(sinx)lnx?

Accepted Answer

Logarithmic differentiation

Advanced Differentiation Techniques in Calculus: Logarithmic and Implicit Differentiation

Study Guide - Practice Questions