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Derivative of:
Derivative of 3x^2-5x+5
Derivative of (1-x^2)^2
Derivative of -1/(x-1)^2
Derivative of y=x^3×cosx
Integral of d{x}:
(1-x^2)^2
Limit of the function:
(1-x^2)^2
Identical expressions
(one -x^ two)^ two
(1 minus x squared ) squared
(one minus x to the power of two) to the power of two
(1-x2)2
1-x22
(1-x²)²
(1-x to the power of 2) to the power of 2
1-x^2^2
Similar expressions
(1+x^2)^2

The derivative of the function/ (1-x^2)^2

Derivative of (1-x^2)^2

The solution

You have entered [src]

        2
/     2\ 
\1 - x /

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

(1 - x^2)^2

Detail solution

Let $u = 1 - x^{2}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - x^{2}\right)$ :
1. Differentiate $1 - x^{2}$ term by term:
  1. The derivative of the constant $1$ is zero.
  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: $- 2 x$
  The result is: $- 2 x$
The result of the chain rule is:

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

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

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

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 (1-x^2)^2