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sqrt(2500-x^2)
The derivative of the function/ sqrt(2500-x^2)

Derivative of sqrt(2500-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___________
  /         2 
\/  2500 - x
$$\sqrt{2500 - x^{2}}$$ 
  /   ___________\
d |  /         2 |
--\\/  2500 - x  /
dx
$$\frac{d}{d x} \sqrt{2500 - x^{2}}$$
Transform
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] 
     -x       
--------------
   ___________
  /         2 
\/  2500 - x
$$- \frac{x}{\sqrt{2500 - x^{2}}}$$
Simplify
The second derivative [src] 
 /         2   \ 
 |        x    | 
-|1 + ---------| 
 |            2| 
 \    2500 - x / 
-----------------
     ___________ 
    /         2  
  \/  2500 - x
$$- \frac{\frac{x^{2}}{2500 - x^{2}} + 1}{\sqrt{2500 - x^{2}}}$$
Simplify
The third derivative [src] 
     /         2   \
     |        x    |
-3*x*|1 + ---------|
     |            2|
     \    2500 - x /
--------------------
              3/2   
   /        2\      
   \2500 - x /
$$- \frac{3 x \left(\frac{x^{2}}{2500 - x^{2}} + 1\right)}{\left(2500 - x^{2}\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(2500-x^2)
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