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Calculate the derivative of the function

g(x) = e^{2x}

May 1, 2024

Calculate the derivative of the function

g(x) = e^{2x}

Generated Graph

Solution by Steps

step 1

To find the derivative of the function

g(x) = e^{2x}

, we use the chain rule

step 2

The derivative of

e^{u}

with respect to

x

e^{u} \frac{du}{dx}

, where

u = 2x

step 3

The derivative of

2x

with respect to

x

is 2

step 4

Applying the chain rule, we multiply the derivative of

e^{u}

by the derivative of

u

to get the derivative of

g(x)

step 5

Therefore, the derivative of

g(x) = e^{2x}

2e^{2x}

Answer

g'(x) = 2e^{2x}

Key Concept

Chain Rule in Differentiation

Explanation

The chain rule is used to differentiate composite functions. In this case,

e^{2x}

is a composite function where

e^{u}

is the outer function and

2x

is the inner function.