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Derivative of:
Derivative of 6^x
Derivative of (x^2-1)/(x^2+1)
Derivative of (x+3)/(x-1)
Derivative of (x-3)^3
Integral of d{x}:
x^2*e^(x^2)
Identical expressions
x^ two *e^(x^ two)
x squared multiply by e to the power of (x squared )
x to the power of two multiply by e to the power of (x to the power of two)
x2*e(x2)
x2*ex2
x²*e^(x²)
x to the power of 2*e to the power of (x to the power of 2)
x^2e^(x^2)
x2e(x2)
x2ex2
x^2e^x^2
Similar expressions
x^2*(e^(x^2))
What you mean?
x^2*e^(x^2)
x^((2*e)^(x^2))
x^((2*e)^(x^2))

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

You entered:

x^2*e^(x^2)

What you mean?

x^2*e^(x^2)

x^((2*e)^(x^2))

x^((2*e)^(x^2))

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

The solution

You have entered [src]

    / 2\
 2  \x /
x *e

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

  /    / 2\\
d | 2  \x /|
--\x *e    /
dx

$$\frac{d}{d x} x^{2} e^{x^{2}}$$

Transform

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
$g{\left(x \right)} = e^{x^{2}}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = x^{2}$ .
2. The derivative of $e^{u}$ is itself.
3. 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 result is: $2 x^{3} e^{x^{2}} + 2 x e^{x^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$2 x^{3} e^{x^{2}} + 2 x e^{x^{2}}$$

Simplify

The second derivative [src]

                              / 2\
  /       2    2 /       2\\  \x /
2*\1 + 4*x  + x *\1 + 2*x //*e

$$2 \left(x^{2} \cdot \left(2 x^{2} + 1\right) + 4 x^{2} + 1\right) e^{x^{2}}$$

Simplify

The third derivative [src]

                                / 2\
    /       2    2 /       2\\  \x /
4*x*\6 + 6*x  + x *\3 + 2*x //*e

$$4 x \left(x^{2} \cdot \left(2 x^{2} + 3\right) + 6 x^{2} + 6\right) e^{x^{2}}$$

Simplify

The graph

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