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Derivative of:
Derivative of x^4*e^x
Derivative of 5^-x
Derivative of x^2*sin(2*x-3)
Derivative of x^2/cosx
Integral of d{x}:
x^4*e^x
Identical expressions
x^ four *e^x
x to the power of 4 multiply by e to the power of x
x to the power of four multiply by e to the power of x
x4*ex
x⁴*e^x
x^4e^x
x4ex

The derivative of the function/ x^4*e^x

Derivative of x^4*e^x

The solution

You have entered [src]

 4  x
x *E

$$e^{x} x^{4}$$

x^4*E^x

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{4}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
$g{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
The result is: $x^{4} e^{x} + 4 x^{3} e^{x}$
Now simplify:

$x^{3} \left(x + 4\right) e^{x}$

The answer is:

$x^{3} \left(x + 4\right) e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 4  x      3  x
x *e  + 4*x *e

$$x^{4} e^{x} + 4 x^{3} e^{x}$$

Simplify

The second derivative [src]

 2 /      2      \  x
x *\12 + x  + 8*x/*e

$$x^{2} \left(x^{2} + 8 x + 12\right) e^{x}$$

Simplify

The third derivative [src]

  /      3       2       \  x
x*\24 + x  + 12*x  + 36*x/*e

$$x \left(x^{3} + 12 x^{2} + 36 x + 24\right) e^{x}$$

Simplify

The graph

Derivative of x^4*e^x