# left f(x)=2^(sin(x))Find f'(x)

left $f\left(x\right)={2}^{\mathrm{sin}\left(x\right)}$
Find f'(x)

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To compute the derivative of the given function (involving exponentials)
Step 2
Here ,we have used chain rule: If $h\left(x\right)=p\left(q\left(x\right)\right)$, then ${h}^{\prime }\left(x\right)={p}^{\prime }\left(q\right)×{q}^{\prime }\left(x\right)$
Write
by chain rule
${f}^{\prime }\left(x\right)=\left({2}^{u}\right)$(derivative wrt u)$×{u}^{\prime }\left(x\right)$
$={2}^{u}\mathrm{ln}\left(2\right)\mathrm{cos}x$
$=\left(\mathrm{ln}2\right){2}^{\mathrm{sin}x}\left(\mathrm{cos}x\right)$

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