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Identical expressions
sqrt(x^ two -3x- ten)
square root of (x squared minus 3x minus 10)
square root of (x to the power of two minus 3x minus ten)
√(x^2-3x-10)
sqrt(x2-3x-10)
sqrtx2-3x-10
sqrt(x²-3x-10)
sqrt(x to the power of 2-3x-10)
sqrtx^2-3x-10
Similar expressions
sqrt(x^2-3x+10)
sqrt(x^2+3x-10)

The derivative of the function/ sqrt(x^2-3x-10)

Derivative of sqrt(x^2-3x-10)

The solution

You have entered [src]

   _______________
  /  2            
\/  x  - 3*x - 10

$$\sqrt{\left(x^{2} - 3 x\right) - 10}$$

sqrt(x^2 - 3*x - 10)

Detail solution

Let $u = \left(x^{2} - 3 x\right) - 10$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(x^{2} - 3 x\right) - 10\right)$ :
1. Differentiate $\left(x^{2} - 3 x\right) - 10$ term by term:
  1. Differentiate $x^{2} - 3 x$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $-3$
    The result is: $2 x - 3$
  2. The derivative of the constant $-10$ is zero.
  The result is: $2 x - 3$
The result of the chain rule is:

$\frac{2 x - 3}{2 \sqrt{\left(x^{2} - 3 x\right) - 10}}$
Now simplify:

$\frac{x - \frac{3}{2}}{\sqrt{x^{2} - 3 x - 10}}$

The answer is:

$\frac{x - \frac{3}{2}}{\sqrt{x^{2} - 3 x - 10}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     -3/2 + x     
------------------
   _______________
  /  2            
\/  x  - 3*x - 10

$$\frac{x - \frac{3}{2}}{\sqrt{\left(x^{2} - 3 x\right) - 10}}$$

Simplify

The second derivative [src]

                 2    
       (-3 + 2*x)     
1 - ------------------
      /       2      \
    4*\-10 + x  - 3*x/
----------------------
    ________________  
   /        2         
 \/  -10 + x  - 3*x

$$\frac{- \frac{\left(2 x - 3\right)^{2}}{4 \left(x^{2} - 3 x - 10\right)} + 1}{\sqrt{x^{2} - 3 x - 10}}$$

Simplify

The third derivative [src]

  /                2  \           
  |      (-3 + 2*x)   |           
3*|-4 + --------------|*(-3 + 2*x)
  |            2      |           
  \     -10 + x  - 3*x/           
----------------------------------
                        3/2       
        /       2      \          
      8*\-10 + x  - 3*x/

$$\frac{3 \left(2 x - 3\right) \left(\frac{\left(2 x - 3\right)^{2}}{x^{2} - 3 x - 10} - 4\right)}{8 \left(x^{2} - 3 x - 10\right)^{\frac{3}{2}}}$$

Simplify

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Derivative of sqrt(x^2-3x-10)

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The solution