Let $y = 2 ^ { \tan x }$ Then dy is

A) $2 ^ { \sec ^ { 2 } x } \ln 2 d x$
B) $2 ^ { \sec ^ { 2 } x } \tan x d x$
C) $2 ^ { \tan x } \sec ^ { 2 } x d x$
D) $2 ^ { \tan x } \sec ^ { 2 } x \ln 2 d x$
E) $- 2 ^ { \tan x } \sec ^ { 2 } x \ln 2 d x$

Question

Let $y = 2 ^ { \tan x }$ Then dy is

A) $2 ^ { \sec ^ { 2 } x } \ln 2 d x$
B) $2 ^ { \sec ^ { 2 } x } \tan x d x$
C) $2 ^ { \tan x } \sec ^ { 2 } x d x$
D) $2 ^ { \tan x } \sec ^ { 2 } x \ln 2 d x$
E) $- 2 ^ { \tan x } \sec ^ { 2 } x \ln 2 d x$

Quizplus · Accepted Answer

To find the derivative $dy$ of $y = 2 ^ { \tan x }$, we use the chain rule. The derivative of $2^u$ with respect to $u$ is $2^u \ln 2$, and the derivative of $\tan x$ with respect to $x$ is $\sec^2 x$. Applying the chain rule, we get $dy = 2^{\tan x} \ln 2 \cdot \sec^2 x dx$, which matches option D.

Let y=2tan⁡xy = 2 ^ { \tan x }y=2tanx Then Dy Is A)

Let $y = 2 ^ { \tan x }$ Then Dy Is

A)