Key to "Find the derivative of y=e5x"

Patricia Crane

Answered question

2021-12-15

Find the derivative of

y = e^{5 x}

Serita Dewitt

Beginner2021-12-16Added 41 answers

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^{5 x}

by the chain rule, the derivative will be equal to the derivative of

e^{5 x}

with respect to

5^{x}

, multiplied by the derivative of

5^{x}

with respect to x.

\frac{d y}{d x} = \frac{d}{d x} [5 x] \times e^{5 x}

\frac{d y}{d x} = 5 e^{5 x}

Chanell Sanborn

Beginner2021-12-17Added 41 answers

\frac{d}{d x} (e^{5 x})

Apply the cahin rule:

= e^{5 x} \frac{d}{d x} (5 x)

\frac{d}{d x} (5 x) = 5

= e^{5 x} \times 5

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