"Find the derivatives of the functions. f(x)=e2x+1" was answered by students like you

Reeves

Answered question

2021-06-11

Find the derivatives of the functions.

f (x) = e^{2 x + 1}

Answer & Explanation

wheezym

Skilled2021-06-12Added 103 answers

Recall the generalized rule for the derivative of exponential function:

\frac{d}{d x} [e^{u}] = e^{u} \frac{d u}{d x}

In this exercise, we want to find the derivative of

f (x) = e^{2 x + 1}

To make use of the rule, denote the argument of the exponential function by u, i.e.
u=2x+1
Using the rule from Step 1, we get:

f^{'} (x) = e^{u} \frac{d u}{d x} = e^{2 x + 1} \frac{d}{d x} (2 x + 1)} = 2

= 2 e^{2 x + 1}

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