Key to "Find the derivative of e2x."

Irrerbthist6n

Answered question

2021-12-11

Find the derivative of

e^{2 x}

enlacamig

Beginner2021-12-12Added 30 answers

\frac{d}{d x} (e^{2 x})

Apply the Chain Rule:

e^{2 x} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

, then we have

= e^{2 x} \times 2

\frac{d}{d x} (e^{2 x}) = e^{2 x} \times 2

Steve Hirano

Beginner2021-12-13Added 34 answers

Use the Chain Rule

\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}

u = f (x) \Rightarrow \frac{d u}{d x} = f^{'} (x)

y = e^{u} \Rightarrow \frac{d y}{d u} = e^{u}

Therefore,

\frac{d y}{d x} = e^{u} \times f^{'} (x) = f^{'} (x) e^{f (x)}

\frac{d}{d x} (e^{f (x)}) = f^{'} (x) e^{f (x)}

With

y = e^{2 x}

we have

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

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