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y=sqrt(25-x^2)
The derivative of the function/ y=sqrt(25-x^2)

Derivative of y=sqrt(25-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   _________
  /       2 
\/  25 - x
−x2+25\sqrt{- x^{2} + 25} 
  /   _________\
d |  /       2 |
--\\/  25 - x  /
dx
ddx−x2+25\frac{d}{d x} \sqrt{- x^{2} + 25}
Transform
Detail solution

  1. Let u=25−x2u = 25 - 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(25−x2)\frac{d}{d x} \left(25 - x^{2}\right):

    1. Differentiate 25−x225 - x^{2} term by term:

      1. The derivative of the constant 2525 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:

    −x25−x2- \frac{x}{\sqrt{25 - x^{2}}}

The answer is:

−x25−x2- \frac{x}{\sqrt{25 - 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 
\/  25 - x
−x−x2+25- \frac{x}{\sqrt{- x^{2} + 25}}
Simplify
The second derivative [src] 
 /        2  \ 
 |       x   | 
-|1 + -------| 
 |          2| 
 \    25 - x / 
---------------
     _________ 
    /       2  
  \/  25 - x
−x2−x2+25+1−x2+25- \frac{\frac{x^{2}}{- x^{2} + 25} + 1}{\sqrt{- x^{2} + 25}}
Simplify
The third derivative [src] 
     /        2  \
     |       x   |
-3*x*|1 + -------|
     |          2|
     \    25 - x /
------------------
            3/2   
   /      2\      
   \25 - x /
−3x(x2−x2+25+1)(−x2+25)32- \frac{3 x \left(\frac{x^{2}}{- x^{2} + 25} + 1\right)}{\left(- x^{2} + 25\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of y=sqrt(25-x^2)
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