If $f ( x ) = 6 ^ { x } \tan x$ , then $f ^ { \prime } ( x ) = \frac { 6 ^ { x } } { \cos ^ { 2 } x } + 6 ^ { x } \cdot \ln 6 \cdot \tan x$ .

Question

Quizplus · Accepted Answer

To find $f'(x)$ for $f(x) = 6^x \tan x$, we use the product rule and the chain rule. The derivative of $6^x$ is $6^x \ln 6$, and the derivative of $\tan x$ is $\sec^2 x = \frac{1}{\cos^2 x}$. Applying the product rule, $f'(x) = 6^x \cdot \frac{1}{\cos^2 x} + 6^x \ln 6 \cdot \tan x$, which matches the given expression.

If f(x)=6xtan⁡xf ( x ) = 6 ^ { x } \tan xf(x)=6xtanx

If $f ( x ) = 6 ^ { x } \tan x$