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Derivative of:
Derivative of e^(2*x)
Derivative of x*acot(x)
Derivative of sin(pi*x)
Derivative of cosy
Identical expressions
y=(one -x^ two)^ five
y equally (1 minus x squared ) to the power of 5
y equally (one minus x to the power of two) to the power of five
y=(1-x2)5
y=1-x25
y=(1-x²)⁵
y=(1-x to the power of 2) to the power of 5
y=1-x^2^5
Similar expressions
y=(1+x^2)^5

The derivative of the function/ y=(1-x^2)^5

Derivative of y=(1-x^2)^5

The solution

You have entered [src]

        5
/     2\ 
\1 - x /

$$\left(- x^{2} + 1\right)^{5}$$

  /        5\
d |/     2\ |
--\\1 - x / /
dx

$$\frac{d}{d x} \left(- x^{2} + 1\right)^{5}$$

Transform

Detail solution

Let $u = 1 - x^{2}$ .
Apply the power rule: $u^{5}$ goes to $5 u^{4}$
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:

$- 10 x \left(1 - x^{2}\right)^{4}$
Now simplify:

$- 10 x \left(x^{2} - 1\right)^{4}$

The answer is:

$- 10 x \left(x^{2} - 1\right)^{4}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              4
      /     2\ 
-10*x*\1 - x /

$$- 10 x \left(- x^{2} + 1\right)^{4}$$

Simplify

The second derivative [src]

             3            
    /      2\  /        2\
-10*\-1 + x / *\-1 + 9*x /

$$- 10 \left(x^{2} - 1\right)^{3} \cdot \left(9 x^{2} - 1\right)$$

Simplify

The third derivative [src]

                2            
       /      2\  /        2\
-240*x*\-1 + x / *\-1 + 3*x /

$$- 240 x \left(x^{2} - 1\right)^{2} \cdot \left(3 x^{2} - 1\right)$$

Simplify

The graph

Derivative of y=(1-x^2)^5