Question
Diffrentiate the following w.r.t.x

$5^{\sin 3 x+3}$

Answer

Let $y=5^{\sin 3 x+3}$

Differentiating w.r.t. x, we get

$\frac{d y}{d x}=\frac{d}{d x}\left(5^{\sin ^3 x+3}\right)$

$\begin{aligned} & =5^{\sin ^3 x+3} \cdot \log 5 \cdot \frac{d}{d x}\left(\sin ^3 x+3\right) \\ & =5^{\sin ^3 x+3} \cdot \log 5 \cdot\left[3 \sin ^2 x \cdot \frac{d}{d x}(\sin x)+0\right] \\ & =5^{\sin ^3 x+3} \cdot \log 5 \cdot\left[3 \sin ^2 x \cos x\right] \\ & =3 \sin ^2 x \cos x \cdot 5^{\sin ^3 x+3} \cdot \log 5\end{aligned}$

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