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  4. If y =( tan x ) sin x , then ( dy / dx ) is equal to

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

Continuity and Differentiability

Solution:

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