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

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

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Answer 1 · 2014-08-04T22:03:03

$\frac{d y}{d x} = 5 e^{5 x}$ $dy/dx = 5e^(5x)$

Process:

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

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

$\frac{d y}{d x} = \frac{d}{d x} [5 x] \cdot e^{5 x}$ $dy/dx = d/dx[5x] * e^(5x)$

$\frac{d y}{d x} = 5 e^{5 x}$ $dy/dx = 5 e^(5x)$

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

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