Mister Exam

Other calculators

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

Derivative of 4/x^3

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
4 
--
 3
x
4x3\frac{4}{x^{3}} 
4/x^3
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=x3u = x^{3}.

    2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

    3. Then, apply the chain rule. Multiply by ddxx3\frac{d}{d x} x^{3}:

      1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

      The result of the chain rule is:

      −3x4- \frac{3}{x^{4}}

    So, the result is: −12x4- \frac{12}{x^{4}}

The answer is:

−12x4- \frac{12}{x^{4}}

The graph
02468-8-6-4-2-1010-200000100000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-12 
----
  4 
 x
−12x4- \frac{12}{x^{4}}
Simplify
The second derivative [src] 
48
--
 5
x
48x5\frac{48}{x^{5}}
Simplify
The third derivative [src] 
-240 
-----
   6 
  x
−240x6- \frac{240}{x^{6}}
Simplify
The graph
Derivative of 4/x^3
    © Mister Exam – Calculator