Question

If $y=(\tan x{)}^{\sin x}$, then $\frac{dy}{dx}$ is equal to

• A. $\sec x+\cos x$
• B. $\sec x+\log$
• C. $(\tan x{)}^{\sin x}$
• D. None of these

Answer 1

Answer: (D)

We have, $y=(\tan x{)}^{\sin x}$
Taking logarithm on both sides
$\log y=\sin x\log (\tan x)$
Differentiating w.r.t. $x$