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The derivative of the function/ √(1-(25x^2))

Derivative of √(1-(25x^2))

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___________
  /         2 
\/  1 - 25*x
$$\sqrt{1 - 25 x^{2}}$$ 
sqrt(1 - 25*x^2)
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. The derivative of the constant 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: goes to

        So, the result is:

      The result is:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -25*x     
--------------
   ___________
  /         2 
\/  1 - 25*x
$$- \frac{25 x}{\sqrt{1 - 25 x^{2}}}$$
Simplify
The second derivative [src] 
    /          2  \
    |      25*x   |
-25*|1 + ---------|
    |            2|
    \    1 - 25*x /
-------------------
      ___________  
     /         2   
   \/  1 - 25*x
$$- \frac{25 \left(\frac{25 x^{2}}{1 - 25 x^{2}} + 1\right)}{\sqrt{1 - 25 x^{2}}}$$
Simplify
The third derivative [src] 
        /          2  \
        |      25*x   |
-1875*x*|1 + ---------|
        |            2|
        \    1 - 25*x /
-----------------------
                3/2    
     /        2\       
     \1 - 25*x /
$$- \frac{1875 x \left(\frac{25 x^{2}}{1 - 25 x^{2}} + 1\right)}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}$$
Simplify
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