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Derivative of:
Derivative of (x^2+1)^3
Derivative of (x+3)/(x-2)
Derivative of u
Derivative of sqrt(4-x^2)
Graphing y =:
e^x*x^3
Limit of the function:
e^x*x^3
Identical expressions
e^x*x^ three
e to the power of x multiply by x cubed
e to the power of x multiply by x to the power of three
ex*x3
e^x*x³
e to the power of x*x to the power of 3
e^xx^3
exx3
Similar expressions
y=e^x*(x^30+30x+1)

The derivative of the function/ e^x*x^3

Derivative of e^x*x^3

The solution

You have entered [src]

 x  3
E *x

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

E^x*x^3

Detail solution

Apply the product rule:

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

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