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Derivative of:
Derivative of x^3*e^x
Derivative of x*e^(2*x)
Derivative of x+4
Derivative of x*acot(x)
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 x
x to the power of three multiply by e to the power of x
x3*ex
x³*e^x
x to the power of 3*e to the power of x
x^3e^x
x3ex
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 product rule:

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

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

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

The answer is:

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

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  + 9*x  + 18*x/*e

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

Simplify

The graph

Derivative of x^3*e^x