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

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∻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 $ u $ is $ e^{u} $, where $ u $ is a function of $ x $. ‖ ‖ step 3 ⋮ Here, $ u = 2x $. The derivative of $ u $ with respect to $ x $ is $ 2 $. ‖ ‖ step 4 ⋮ Applying the chain rule, the derivative of $ g(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. The derivative is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.⚹◊What is the general formula for calculating the derivative of $e^{ax}$?⍭ Generate me a similar question◊

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