Mister Exam

Other calculators

x^4-x^2
The derivative of the function/ x^4-x^2

Derivative of x^4-x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 4    2
x  - x
x4−x2x^{4} - x^{2} 
x^4 - x^2
Detail solution

  1. Differentiate x4−x2x^{4} - x^{2} term by term:

    1. Apply the power rule: x4x^{4} goes to 4x34 x^{3}

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

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      So, the result is: −2x- 2 x

    The result is: 4x3−2x4 x^{3} - 2 x

The answer is:

4x3−2x4 x^{3} - 2 x

The graph
02468-8-6-4-2-101020000-10000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
          3
-2*x + 4*x
4x3−2x4 x^{3} - 2 x
Simplify
The second derivative [src] 
  /        2\
2*\-1 + 6*x /
2(6x2−1)2 \left(6 x^{2} - 1\right)
Simplify
The third derivative [src] 
24*x
24x24 x
Simplify
The graph
Derivative of x^4-x^2
    © Mister Exam – Calculator