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Derivative of:
Derivative of f(x)=2x-3
Derivative of 2*cos(x)+sin(x)
Derivative of (1-x^2)^10
Derivative of (-1)/x+4*x^2
Identical expressions
(one -x^ two)^ ten
(1 minus x squared ) to the power of 10
(one minus x to the power of two) to the power of ten
(1-x2)10
1-x210
(1-x²)^10
(1-x to the power of 2) to the power of 10
1-x^2^10
Similar expressions
(1+x^2)^10

The derivative of the function/ (1-x^2)^10

Derivative of (1-x^2)^10

The solution

You have entered [src]

        10
/     2\  
\1 - x /

$$\left(1 - x^{2}\right)^{10}$$

  /        10\
d |/     2\  |
--\\1 - x /  /
dx

$$\frac{d}{d x} \left(1 - x^{2}\right)^{10}$$

Transform

Detail solution

Let $u = 1 - x^{2}$ .
Apply the power rule: $u^{10}$ goes to $10 u^{9}$
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:

$- 20 x \left(1 - x^{2}\right)^{9}$
Now simplify:

$20 x \left(x^{2} - 1\right)^{9}$

The answer is:

$20 x \left(x^{2} - 1\right)^{9}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              9
      /     2\ 
-20*x*\1 - x /

$$- 20 x \left(1 - x^{2}\right)^{9}$$

Simplify

The second derivative [src]

            8             
   /      2\  /         2\
20*\-1 + x / *\-1 + 19*x /

$$20 \left(x^{2} - 1\right)^{8} \cdot \left(19 x^{2} - 1\right)$$

Simplify

The third derivative [src]

               7             
      /      2\  /         2\
360*x*\-1 + x / *\-3 + 19*x /

$$360 x \left(x^{2} - 1\right)^{7} \cdot \left(19 x^{2} - 3\right)$$

Simplify

The graph

Derivative of (1-x^2)^10