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Derivative of:
Derivative of e^(7*x)
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Graphing y =:
x^4-4*x^2
Limit of the function:
x^4-4*x^2
Identical expressions
x^ four - four *x^ two
x to the power of 4 minus 4 multiply by x squared
x to the power of four minus four multiply by x to the power of two
x4-4*x2
x⁴-4*x²
x to the power of 4-4*x to the power of 2
x^4-4x^2
x4-4x2
Similar expressions
x^4+4*x^2

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

Derivative of x^4-4*x^2

The solution

You have entered [src]

 4      2
x  - 4*x

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

x^4 - 4*x^2

Detail solution

Differentiate $x^{4} - 4 x^{2}$ 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: $- 8 x$
The result is: $4 x^{3} - 8 x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          3
-8*x + 4*x

$$4 x^{3} - 8 x$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify