 # Find the derivative of y=e^{5x} Patricia Crane 2021-12-15 Answered
Find the derivative of $y={e}^{5x}$
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The derivative of ${e}^{x}$ is simply ${e}^{x}$. However, x has a coefficient, so you have to use the chain rule.
If $y={e}^{5x}$ by the chain rule, the derivative will be equal to the derivative of ${e}^{5x}$ with respect to ${5}^{x}$, multiplied by the derivative of ${5}^{x}$ with respect to x.
$\frac{dy}{dx}=\frac{d}{dx}\left[5x\right]×{e}^{5x}$
$\frac{dy}{dx}=5{e}^{5x}$

We have step-by-step solutions for your answer! Chanell Sanborn
$\frac{d}{dx}\left({e}^{5x}\right)$
Apply the cahin rule:
$={e}^{5x}\frac{d}{dx}\left(5x\right)$
$\frac{d}{dx}\left(5x\right)=5$
$={e}^{5x}×5$

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