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Derivative of:
Derivative of cos(x)^(25)
Derivative of ch(x)
Derivative of tgx^2
Derivative of sqrt(x^2-25)
Graphing y =:
sqrt(x^2-25)
Identical expressions
sqrt(x^ two - twenty-five)
square root of (x squared minus 25)
square root of (x to the power of two minus twenty minus five)
√(x^2-25)
sqrt(x2-25)
sqrtx2-25
sqrt(x²-25)
sqrt(x to the power of 2-25)
sqrtx^2-25
Similar expressions
sqrt(x^2+25)

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

Derivative of sqrt(x^2-25)

The solution

You have entered [src]

   _________
  /  2      
\/  x  - 25

$$\sqrt{x^{2} - 25}$$

sqrt(x^2 - 25)

Detail solution

Let $u = x^{2} - 25$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 25\right)$ :
1. Differentiate $x^{2} - 25$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $-25$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{x}{\sqrt{x^{2} - 25}}$
Now simplify:

$\frac{x}{\sqrt{x^{2} - 25}}$

The answer is:

$\frac{x}{\sqrt{x^{2} - 25}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x      
------------
   _________
  /  2      
\/  x  - 25

$$\frac{x}{\sqrt{x^{2} - 25}}$$

Simplify

The second derivative [src]

         2   
        x    
 1 - --------
            2
     -25 + x 
-------------
   __________
  /        2 
\/  -25 + x

$$\frac{- \frac{x^{2}}{x^{2} - 25} + 1}{\sqrt{x^{2} - 25}}$$

Simplify

The third derivative [src]

    /         2   \
    |        x    |
3*x*|-1 + --------|
    |            2|
    \     -25 + x /
-------------------
             3/2   
   /       2\      
   \-25 + x /

$$\frac{3 x \left(\frac{x^{2}}{x^{2} - 25} - 1\right)}{\left(x^{2} - 25\right)^{\frac{3}{2}}}$$

Simplify

The graph

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Derivative of sqrt(x^2-25)

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The solution