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Derivative of:
Derivative of x^2*e^x
Derivative of x^2*e^(-x)
Derivative of sqrt(2*x)
Derivative of -sin(x)
Integral of d{x}:
x^2*e^x
Graphing y =:
x^2*e^x
Identical expressions
x^ two *e^x
x squared multiply by e to the power of x
x to the power of two multiply by e to the power of x
x2*ex
x²*e^x
x to the power of 2*e to the power of x
x^2e^x
x2ex
Similar expressions
x^2*(e^(x^2))
cot(3*x)^(2*e^x)

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

Derivative of x^2*e^x

The solution

You have entered [src]

 2  x
x *E

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

x^2*E^x

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 $2 x$
$g{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
The result is: $x^{2} e^{x} + 2 x e^{x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2  x        x
x *e  + 2*x*e

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of x^2*e^x