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Derivative of:
Derivative of e^(2-x)
Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
Derivative of (2*x-1)^2
Derivative of 2/(x^2-1)
Graphing y =:
4*x^2-x^4
Identical expressions
four *x^ two -x^ four
4 multiply by x squared minus x to the power of 4
four multiply by x to the power of two minus x to the power of four
4*x2-x4
4*x²-x⁴
4*x to the power of 2-x to the power of 4
4x^2-x^4
4x2-x4
Similar expressions
4*x^2+x^4

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

Derivative of 4*x^2-x^4

The solution

You have entered [src]

   2    4
4*x  - x

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

4*x^2 - x^4

Detail solution

Differentiate $- x^{4} + 4 x^{2}$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $8 x$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $- 4 x^{3}$
The result is: $- 4 x^{3} + 8 x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     3      
- 4*x  + 8*x

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

-24*x

$$- 24 x$$

Simplify

The graph

Derivative of 4*x^2-x^4