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Derivative of:
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Derivative of sqrt(x)*log(x)
Identical expressions
sqrt(x^ two - thirty-six)
square root of (x squared minus 36)
square root of (x to the power of two minus thirty minus six)
√(x^2-36)
sqrt(x2-36)
sqrtx2-36
sqrt(x²-36)
sqrt(x to the power of 2-36)
sqrtx^2-36
Similar expressions
sqrt(x^2+36)

The derivative of the function/ sqrt(x^2-36)

Derivative of sqrt(x^2-36)

The solution

You have entered [src]

   _________
  /  2      
\/  x  - 36

$$\sqrt{x^{2} - 36}$$

  /   _________\
d |  /  2      |
--\\/  x  - 36 /
dx

$$\frac{d}{d x} \sqrt{x^{2} - 36}$$

Transform

Detail solution

Let $u = x^{2} - 36$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 36\right)$ :
1. Differentiate $x^{2} - 36$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $\left(-1\right) 36$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{x}{\sqrt{x^{2} - 36}}$
Now simplify:

$\frac{x}{\sqrt{x^{2} - 36}}$

The answer is:

$\frac{x}{\sqrt{x^{2} - 36}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x      
------------
   _________
  /  2      
\/  x  - 36

$$\frac{x}{\sqrt{x^{2} - 36}}$$

Simplify

The second derivative [src]

         2   
        x    
 1 - --------
            2
     -36 + x 
-------------
   __________
  /        2 
\/  -36 + x

$$\frac{- \frac{x^{2}}{x^{2} - 36} + 1}{\sqrt{x^{2} - 36}}$$

Simplify

The third derivative [src]

    /         2   \
    |        x    |
3*x*|-1 + --------|
    |            2|
    \     -36 + x /
-------------------
             3/2   
   /       2\      
   \-36 + x /

$$\frac{3 x \left(\frac{x^{2}}{x^{2} - 36} - 1\right)}{\left(x^{2} - 36\right)^{\frac{3}{2}}}$$

Simplify

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Derivative of sqrt(x^2-36)

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The solution