# Calculating derivatives Find the derivative of the following functions. y=\sin x+4^{ex}

Calculating derivatives Find the derivative of the following functions.
$y=\mathrm{sin}x+{4}^{ex}$
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Step 1
Given function:
$y=\mathrm{sin}x+{4}^{ex}$
Taking derivative with respect to x :
$\frac{dy}{dx}=\frac{d}{dx}\left(\mathrm{sin}x+4{e}^{x}\right)$
$\frac{dy}{dx}=\frac{d}{dx}\left(\mathrm{sin}x\right)+4\frac{d}{dx}\left({e}^{x}\right)$
Step 2
Using the rules of derivative:
$\frac{dy}{dx}=\mathrm{cos}x+4{e}^{x}$
Hence,
The derivative of the following function is :
${y}^{\prime }\left(x\right)=\mathrm{cos}x+4{e}^{x}$