Barcoo12tc

2023-03-24

How to find the derivative of $y={e}^{5x}$?

Tiffany Griffin

Beginner2023-03-25Added 4 answers

Process:

The derivative of $e}^{x$ is simply $e}^{x$. However, in this example, x has a coefficient, so we will need to use the chain rule.

If $y={e}^{5x}$, then, by the chain rule, the derivative will be equal to the derivative of $e}^{5x$ with respect to 5x, multiplied by the derivative of 5x with respect to x.

$\frac{dy}{dx}=\frac{d}{dx}\left[5x\right]\cdot {e}^{5x}$

$\frac{dy}{dx}=5{e}^{5x}$

The derivative of $e}^{x$ is simply $e}^{x$. However, in this example, x has a coefficient, so we will need to use the chain rule.

If $y={e}^{5x}$, then, by the chain rule, the derivative will be equal to the derivative of $e}^{5x$ with respect to 5x, multiplied by the derivative of 5x with respect to x.

$\frac{dy}{dx}=\frac{d}{dx}\left[5x\right]\cdot {e}^{5x}$

$\frac{dy}{dx}=5{e}^{5x}$

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