Explained: "Find the first derivative of ex2"

Deragz

Answered question

2021-12-09

Find the first derivative of

e^{x^{2}}

Durst37

Beginner2021-12-10Added 37 answers

e^{x^{2}}

The derivative of

y = e^{f (x)}

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

f (x) = x^{2}

in this case, and the derivative of

x^{2}

is 2x

∴ f^{'} (x) = 2 x

, and

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

Buck Henry

Beginner2021-12-11Added 33 answers

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

Apply the Chain Rule:

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

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

= e^{x^{2}} \times 2 x

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