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Derivative of:
Derivative of 6
Derivative of x*e^x^2
Derivative of (x+4)^2*(x+1)+9
Derivative of (x+3)/(x-1)
Integral of d{x}:
x^3*e^(-x)
Graphing y =:
x^3*e^(-x)
Identical expressions
x^ three *e^(-x)
x cubed multiply by e to the power of ( minus x)
x to the power of three multiply by e to the power of ( minus x)
x3*e(-x)
x3*e-x
x³*e^(-x)
x to the power of 3*e to the power of (-x)
x^3e^(-x)
x3e(-x)
x3e-x
x^3e^-x
Similar expressions
x^3*e^(x)
What you mean?
x^3/e^x
x^((3*e)^(-x))
x^((3*e)^(-x))

The derivative of the function/ x^3*e^(-x)

You entered:

x^3*e^(-x)

What you mean?

x^3/e^x

x^((3*e)^(-x))

x^((3*e)^(-x))

Derivative of x^3*e^(-x)

The solution

You have entered [src]

 3  -x
x *e

$$x^{3} e^{- x}$$

d / 3  -x\
--\x *e  /
dx

$$\frac{d}{d x} x^{3} e^{- x}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{3}$ and $g{\left(x \right)} = e^{x}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
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:

$\left(- x^{3} e^{x} + 3 x^{2} e^{x}\right) e^{- 2 x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3  -x      2  -x
- x *e   + 3*x *e

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

/     3             2\  -x
\6 - x  - 18*x + 9*x /*e

$$\left(- x^{3} + 9 x^{2} - 18 x + 6\right) e^{- x}$$

Simplify

The graph

Derivative of x^3*e^(-x)