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Derivative of e^(x^2)

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E

$$e^{x^{2}}$$

E^(x^2)

Detail solution

Let $u = x^{2}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
The result of the chain rule is:

$2 x e^{x^{2}}$

The answer is:

$2 x e^{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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     \x /
2*x*e

$$2 x e^{x^{2}}$$

Simplify

The second derivative [src]

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  /       2\  \x /
2*\1 + 2*x /*e

$$2 \left(2 x^{2} + 1\right) e^{x^{2}}$$

Simplify

The third derivative [src]

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    /       2\  \x /
4*x*\3 + 2*x /*e

$$4 x \left(2 x^{2} + 3\right) e^{x^{2}}$$

Simplify

The graph