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sqrt(81-x^2)
The derivative of the function/ sqrt(81-x^2)

Derivative of sqrt(81-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   _________
  /       2 
\/  81 - x
$$\sqrt{- x^{2} + 81}$$ 
  /   _________\
d |  /       2 |
--\\/  81 - x  /
dx
$$\frac{d}{d x} \sqrt{- x^{2} + 81}$$
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 
\/  81 - x
$$- \frac{x}{\sqrt{- x^{2} + 81}}$$
Simplify
The second derivative [src] 
 /        2  \ 
 |       x   | 
-|1 + -------| 
 |          2| 
 \    81 - x / 
---------------
     _________ 
    /       2  
  \/  81 - x
$$- \frac{\frac{x^{2}}{- x^{2} + 81} + 1}{\sqrt{- x^{2} + 81}}$$
Simplify
The third derivative [src] 
     /        2  \
     |       x   |
-3*x*|1 + -------|
     |          2|
     \    81 - x /
------------------
            3/2   
   /      2\      
   \81 - x /
$$- \frac{3 x \left(\frac{x^{2}}{- x^{2} + 81} + 1\right)}{\left(- x^{2} + 81\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(81-x^2)
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