Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^x^x
Derivative of y=5x-6
Derivative of (x^4+5)^cot(x)
Derivative of x^3/2x+4
Identical expressions
x^ three /2x+ four
x cubed divide by 2x plus 4
x to the power of three divide by 2x plus four
x3/2x+4
x³/2x+4
x to the power of 3/2x+4
x^3 divide by 2x+4
Similar expressions
x^3/2x-4

The derivative of the function/ x^3/2x+4

Derivative of x^3/2x+4

The solution

You have entered [src]

 3      
x       
--*x + 4
2

$$x \frac{x^{3}}{2} + 4$$

(x^3/2)*x + 4

Detail solution

Differentiate $x \frac{x^{3}}{2} + 4$ term by term:
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x^{4}$ and $g{\left(x \right)} = 2$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. The derivative of the constant $2$ is zero.
  Now plug in to the quotient rule:
  
  $2 x^{3}$
2. The derivative of the constant $4$ is zero.
The result is: $2 x^{3}$

The answer is:

$2 x^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$\frac{x^{3}}{2} + \frac{3 x^{3}}{2}$$

Simplify

The second derivative [src]

   2
6*x

$$6 x^{2}$$

Simplify

The third derivative [src]

12*x

$$12 x$$

Simplify

The graph

Derivative of x^3/2x+4