Question Detail

MTH 102 Differentiation Objective Question

Question

What is the derivative of \( y = e^{\tan x} \)?
Options
A \( e^{\tan x} \sec^2 x \)
Correct Answer
B \( e^{\tan x} \)
C \( \tan x e^{\tan x - 1} \)
D \( \sec^2 x \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

Derivative of ( e^u ) is ( e^u u' ). Here ( u = \tan x ), so ( u' = \sec^2 x ).

Hint

Recall the derivative of the tangent function as the internal derivative.

Question Info