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Calculate the derivative of the function

g(x) = e^{2x}

Jan 4, 2024

Calculate the derivative of the function

g(x) = e^{2x}

Solution by Steps

step 1

To calculate the derivative of the function

g(x) = e^{2x}

, we use the chain rule for differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function

step 2

The outer function is

e^u

where

u = 2x

. The derivative of

e^u

with respect to

u

e^u

step 3

The inner function is

u = 2x

. The derivative of

u

with respect to

x

2

step 4

Applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function:

\frac{d}{dx}e^{2x} = e^{2x} \cdot 2.

Answer

\frac{d}{dx}e^{2x} = 2e^{2x}

Key Concept

Chain Rule for Differentiation

Explanation

The derivative of

e^{2x}

is found by applying the chain rule, which in this case multiplies the original function by the derivative of the exponent.