I need help with exponential functions. I know that the derivative of

Ann Tice

Ann Tice

Answered question

2021-11-16

I need help with exponential functions. I know that the derivative of ex is ex, but wolfram alpha shows a different answer to my function below. If you, for example, take the derivative of e2x do you get 2e2x or e2x?

Answer & Explanation

Witheyesse47

Witheyesse47

Beginner2021-11-17Added 14 answers

You have to use the chain rule here. Writing f(x)=ex and g(x)=2x we have h(x)=f(g(x))=e2x, hence by the chain rule
h(x)=f(g(x))g(x)
Now f(x)=ex, hence f(g(x))=e2x, and g(x)=2, this gives
h(x)=f(g(x))g(x)=e2x(2)=2e2x

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