Question

Math

Posted 7 months ago

`Calculate the derivative of the function $g(x) = e^{2x}$.`

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Answer from Sia

Posted 7 months ago

Solution by Steps

step 1

To find the derivative of the function $g(x) = e^{2x}$, we apply the chain rule

step 2

The derivative of $e^{u}$ with respect to $u$ is $e^{u}$, where $u$ is a function of $x$

step 3

In our case, $u = 2x$. The derivative of $u$ with respect to $x$ is $2$

step 4

Therefore, the derivative of $g(x)$ with respect to $x$ is $2e^{2x}$

Answer

$\frac{d}{dx}g(x) = 2e^{2x}$

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 $u = 2x$ is the inner function.

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