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x^4-8x^2
The derivative of the function/ x^4-8x^2

Derivative of x^4-8x^2

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

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The solution

You have entered [src] 
 4      2
x  - 8*x
x4−8x2x^{4} - 8 x^{2} 
d / 4      2\
--\x  - 8*x /
dx
ddx(x4−8x2)\frac{d}{d x} \left(x^{4} - 8 x^{2}\right)
Transform
Detail solution

  1. Differentiate x4−8x2x^{4} - 8 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. 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: 16x16 x

      So, the result is: −16x- 16 x

    The result is: 4x3−16x4 x^{3} - 16 x

  2. Now simplify:

    4x(x2−4)4 x \left(x^{2} - 4\right)

The answer is:

4x(x2−4)4 x \left(x^{2} - 4\right)

The graph
02468-8-6-4-2-1010-1000010000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           3
-16*x + 4*x
4x3−16x4 x^{3} - 16 x
Simplify
The second derivative [src] 
  /        2\
4*\-4 + 3*x /
4⋅(3x2−4)4 \cdot \left(3 x^{2} - 4\right)
Simplify
The third derivative [src] 
24*x
24x24 x
Simplify
The graph
Derivative of x^4-8x^2
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