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Derivative of:
Derivative of 2*sqrt(x)
Derivative of x^2*e^(-x)
Derivative of sin(3*x)
Derivative of cot(x)*cos(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 ( minus x)
x to the power of two multiply by e to the power of ( minus x)
x2*e(-x)
x2*e-x
x²*e^(-x)
x to the power of 2*e to the power of (-x)
x^2e^(-x)
x2e(-x)
x2e-x
x^2e^-x
Similar expressions
ax^2e^(-x/2)
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 quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2}$ and $g{\left(x \right)} = e^{x}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
Now plug in to the quotient rule:

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

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

The answer is:

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

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)