Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^3+1/x-1
Derivative of x^2/cosx
Derivative of x^2/2x+1
Derivative of sin(x)+cot(x)
Graphing y =:
e^x*x^5
Integral of d{x}:
e^x*x^5
Limit of the function:
e^x*x^5
Identical expressions
e^x*x^ five
e to the power of x multiply by x to the power of 5
e to the power of x multiply by x to the power of five
ex*x5
e^x*x⁵
e^xx^5
exx5

The derivative of the function/ e^x*x^5

Derivative of e^x*x^5

The solution

You have entered [src]

 x  5
E *x

$$e^{x} x^{5}$$

E^x*x^5

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.
$g{\left(x \right)} = x^{5}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
The result is: $x^{5} e^{x} + 5 x^{4} e^{x}$
Now simplify:

$x^{4} \left(x + 5\right) e^{x}$

The answer is:

$x^{4} \left(x + 5\right) e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 5  x      4  x
x *e  + 5*x *e

$$x^{5} e^{x} + 5 x^{4} e^{x}$$

Simplify

The second derivative [src]

 3 /      2       \  x
x *\20 + x  + 10*x/*e

$$x^{3} \left(x^{2} + 10 x + 20\right) e^{x}$$

Simplify

The third derivative [src]

 2 /      3       2       \  x
x *\60 + x  + 15*x  + 60*x/*e

$$x^{2} \left(x^{3} + 15 x^{2} + 60 x + 60\right) e^{x}$$

Simplify

The graph

Derivative of e^x*x^5