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Derivative of:
Derivative of sqrt(x^2-8)
Derivative of ln(1+3x)
Derivative of 16
Derivative of lnx^4
Identical expressions
sqrt(x^ two - eight)
square root of (x squared minus 8)
square root of (x to the power of two minus eight)
√(x^2-8)
sqrt(x2-8)
sqrtx2-8
sqrt(x²-8)
sqrt(x to the power of 2-8)
sqrtx^2-8
Similar expressions
sqrt(x^2+8)
-sqrtx^2-8x+17

The derivative of the function/ sqrt(x^2-8)

Derivative of sqrt(x^2-8)

The solution

You have entered [src]

   ________
  /  2     
\/  x  - 8

$$\sqrt{x^{2} - 8}$$

sqrt(x^2 - 8)

Detail solution

Let $u = x^{2} - 8$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 8\right)$ :
1. Differentiate $x^{2} - 8$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $-8$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{x}{\sqrt{x^{2} - 8}}$
Now simplify:

$\frac{x}{\sqrt{x^{2} - 8}}$

The answer is:

$\frac{x}{\sqrt{x^{2} - 8}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x     
-----------
   ________
  /  2     
\/  x  - 8

$$\frac{x}{\sqrt{x^{2} - 8}}$$

Simplify

The second derivative [src]

        2   
       x    
1 - ------- 
          2 
    -8 + x  
------------
   _________
  /       2 
\/  -8 + x

$$\frac{- \frac{x^{2}}{x^{2} - 8} + 1}{\sqrt{x^{2} - 8}}$$

Simplify

The third derivative [src]

    /         2  \
    |        x   |
3*x*|-1 + -------|
    |           2|
    \     -8 + x /
------------------
            3/2   
   /      2\      
   \-8 + x /

$$\frac{3 x \left(\frac{x^{2}}{x^{2} - 8} - 1\right)}{\left(x^{2} - 8\right)^{\frac{3}{2}}}$$

Simplify

The graph

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Derivative of sqrt(x^2-8)

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The solution