Derivative of e^x^4

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 / 4\
 \x /
e

$$e^{x^{4}}$$

  / / 4\\
d | \x /|
--\e    /
dx

$$\frac{d}{d x} e^{x^{4}}$$

Transform

Detail solution

Let $u = x^{4}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{4}$ :
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
The result of the chain rule is:

$4 x^{3} e^{x^{4}}$

The answer is:

$4 x^{3} e^{x^{4}}$

The graph

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The first derivative [src]

      / 4\
   3  \x /
4*x *e

$$4 x^{3} e^{x^{4}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

                        / 4\
    /       8       4\  \x /
8*x*\3 + 8*x  + 18*x /*e

$$8 x \left(8 x^{8} + 18 x^{4} + 3\right) e^{x^{4}}$$

Simplify

The graph