Mister Exam

Other calculators

f(x)=1/8x^8-x^4
The derivative of the function/ f(x)=1/8x^8-x^4

Derivative of f(x)=1/8x^8-x^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 8     
x     4
-- - x 
8
$$\frac{x^{8}}{8} - x^{4}$$ 
  / 8     \
d |x     4|
--|-- - x |
dx\8      /
$$\frac{d}{d x} \left(\frac{x^{8}}{8} - x^{4}\right)$$
Transform
Detail solution

  1. Differentiate term by term:

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

      1. Apply the power rule: goes to

      So, the result is:

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

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 7      3
x  - 4*x
$$x^{7} - 4 x^{3}$$
Simplify
The second derivative [src] 
 2 /         4\
x *\-12 + 7*x /
$$x^{2} \cdot \left(7 x^{4} - 12\right)$$
Simplify
The third derivative [src] 
    /        4\
6*x*\-4 + 7*x /
$$6 x \left(7 x^{4} - 4\right)$$
Simplify
The graph
Derivative of f(x)=1/8x^8-x^4
    © Mister Exam – Calculator