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Derivative of:
Derivative of 4/x^2
Derivative of cos(x^3)
Derivative of (cos(x))^3
Derivative of 1/tan(x)
Integral of d{x}:
(e^(2x)^2)
Identical expressions
(e^(two x)^2)
(e to the power of (2x) squared )
(e to the power of (two x) squared )
(e(2x)2)
e2x2
(e^(2x)²)
(e to the power of (2x) to the power of 2)
e^2x^2

The derivative of the function/ (e^(2x)^2)

Derivative of (e^(2x)^2)

The solution

You have entered [src]

 /     2\
 \(2*x) /
E

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

E^((2*x)^2)

Detail solution

Let $u = \left(2 x\right)^{2}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x\right)^{2}$ :
1. Let $u = 2 x$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $2$
  The result of the chain rule is:
  
  $8 x$
The result of the chain rule is:

$8 x e^{\left(2 x\right)^{2}}$
Now simplify:

$8 x e^{4 x^{2}}$

The answer is:

$8 x e^{4 x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     /     2\
     \(2*x) /
8*x*e

$$8 x e^{\left(2 x\right)^{2}}$$

Simplify

The second derivative [src]

              /     2\
  /       2\  \(2*x) /
8*\1 + 8*x /*e

$$8 \left(8 x^{2} + 1\right) e^{\left(2 x\right)^{2}}$$

Simplify

The third derivative [src]

                 /     2\
     /       2\  \(2*x) /
64*x*\3 + 8*x /*e

$$64 x \left(8 x^{2} + 3\right) e^{\left(2 x\right)^{2}}$$

Simplify