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sqrt(10-x^2)
The derivative of the function/ sqrt(10-x^2)

Derivative of sqrt(10-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   _________
  /       2 
\/  10 - x
10−x2\sqrt{10 - x^{2}} 
sqrt(10 - x^2)
Detail solution

  1. Let u=10−x2u = 10 - 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(10−x2)\frac{d}{d x} \left(10 - x^{2}\right):

    1. Differentiate 10−x210 - x^{2} term by term:

      1. The derivative of the constant 1010 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:

    −x10−x2- \frac{x}{\sqrt{10 - x^{2}}}

The answer is:

−x10−x2- \frac{x}{\sqrt{10 - 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 
\/  10 - x
−x10−x2- \frac{x}{\sqrt{10 - x^{2}}}
Simplify
The second derivative [src] 
 /        2  \ 
 |       x   | 
-|1 + -------| 
 |          2| 
 \    10 - x / 
---------------
     _________ 
    /       2  
  \/  10 - x
−x210−x2+110−x2- \frac{\frac{x^{2}}{10 - x^{2}} + 1}{\sqrt{10 - x^{2}}}
Simplify
The third derivative [src] 
     /        2  \
     |       x   |
-3*x*|1 + -------|
     |          2|
     \    10 - x /
------------------
            3/2   
   /      2\      
   \10 - x /
−3x(x210−x2+1)(10−x2)32- \frac{3 x \left(\frac{x^{2}}{10 - x^{2}} + 1\right)}{\left(10 - x^{2}\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of sqrt(10-x^2)
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