Question

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

Answer 1

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