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

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the derivative of the function $g(x) = e^{2x}$, we use the chain rule. ‖ ‖ step 2 ⋮ The chain rule states that if $y = f(u)$ and $u = g(x)$, then $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$. ‖ ‖ step 3 ⋮ Here, $f(u) = e^u$ and $u = 2x$. So, $\frac{dy}{du} = e^u$ and $\frac{du}{dx} = 2$. ‖ ‖ step 4 ⋮ Applying the chain rule: $\frac{d}{dx}(e^{2x}) = e^{2x} \cdot 2 = 2e^{2x}$. ‖ ∻Answer∻ ⚹ The derivative of $g(x) = e^{2x}$ is $2e^{2x}$. ⚹ ∻Key Concept∻ ⚹Chain Rule⚹ ∻Explanation∻ ⚹The chain rule is used to differentiate composite functions. In this case, $e^{2x}$ is a composite function where the outer function is $e^u$ and the inner function is $2x$.⚹◊What is the derivative of $e^{2x}$⍭ Generate me a similar question◊

Sia