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Q.
If $y=\left(tanx\right)^{sinx}$, then $\frac{dy}{dx}$ is equal to
Continuity and Differentiability
Solution:
We have, $y = (tanx)^{sinx}$
Taking log on both sides, we get
$logy = sinx \,log(tanx)$
Differentiating $w$.$r$.$t$. $x$, we get
$\frac{1}{y} \frac{dy}{dx}=\frac{sin\,x}{tan\,x}\cdot sec^{2}x+cosx\,log\left(tanx\right)$
$=\left(tanx\right)^{sinx}\left[sec\,x+cosx\left(log\,tan\,x\right)\right]$