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sqrt(100-x^2)
The derivative of the function/ sqrt(100-x^2)

Derivative of sqrt(100-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   __________
  /        2 
\/  100 - x
−x2+100\sqrt{- x^{2} + 100} 
  /   __________\
d |  /        2 |
--\\/  100 - x  /
dx
ddx−x2+100\frac{d}{d x} \sqrt{- x^{2} + 100}
Transform
Detail solution

  1. Let u=100−x2u = 100 - x^{2}.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx(100−x2)\frac{d}{d x} \left(100 - x^{2}\right):

    1. Differentiate 100−x2100 - x^{2} term by term:

      1. The derivative of the constant 100100 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: x2x^{2} goes to 2x2 x

        So, the result is: −2x- 2 x

      The result is: −2x- 2 x

    The result of the chain rule is:

    −x100−x2- \frac{x}{\sqrt{100 - x^{2}}}

The answer is:

−x100−x2- \frac{x}{\sqrt{100 - x^{2}}}

The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     -x      
-------------
   __________
  /        2 
\/  100 - x
−x−x2+100- \frac{x}{\sqrt{- x^{2} + 100}}
Simplify
The second derivative [src] 
 /        2   \ 
 |       x    | 
-|1 + --------| 
 |           2| 
 \    100 - x / 
----------------
    __________  
   /        2   
 \/  100 - x
−x2−x2+100+1−x2+100- \frac{\frac{x^{2}}{- x^{2} + 100} + 1}{\sqrt{- x^{2} + 100}}
Simplify
The third derivative [src] 
     /        2   \
     |       x    |
-3*x*|1 + --------|
     |           2|
     \    100 - x /
-------------------
             3/2   
   /       2\      
   \100 - x /
−3x(x2−x2+100+1)(−x2+100)32- \frac{3 x \left(\frac{x^{2}}{- x^{2} + 100} + 1\right)}{\left(- x^{2} + 100\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of sqrt(100-x^2)
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