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Derivative of:
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Graphing y =:
x^4-2x^2
Identical expressions
x^ four - two x^2
x to the power of 4 minus 2x squared
x to the power of four minus two x squared
x4-2x2
x⁴-2x²
x to the power of 4-2x to the power of 2
Similar expressions
x^4-2*x^2+1
x^4+2x^2

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

Derivative of x^4-2x^2

The solution

You have entered [src]

 4      2
x  - 2*x

$$x^{4} - 2 x^{2}$$

x^4 - 2*x^2

Detail solution

Differentiate $x^{4} - 2 x^{2}$ term by term:
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $- 4 x$
The result is: $4 x^{3} - 4 x$
Now simplify:

$4 x \left(x^{2} - 1\right)$

The answer is:

$4 x \left(x^{2} - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          3
-4*x + 4*x

$$4 x^{3} - 4 x$$

Simplify

The second derivative [src]

  /        2\
4*\-1 + 3*x /

$$4 \left(3 x^{2} - 1\right)$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

Derivative of x^4-2x^2