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Derivative of:
Derivative of x^sqrt(x)
Derivative of log(x+2)
Derivative of ex^2
Derivative of e^(sin(x)-2*x^3)
Identical expressions
one /(two sqrtx^2-6x+ eleven)
1 divide by (2 square root of x squared minus 6x plus 11)
one divide by (two square root of x squared minus 6x plus eleven)
1/(2√x^2-6x+11)
1/(2sqrtx2-6x+11)
1/2sqrtx2-6x+11
1/(2sqrtx²-6x+11)
1/(2sqrtx to the power of 2-6x+11)
1/2sqrtx^2-6x+11
1 divide by (2sqrtx^2-6x+11)
Similar expressions
1/(2sqrtx^2+6x+11)
1/(2sqrtx^2-6x-11)

The derivative of the function/ 1/(2sqrtx^2-6x+11)

Derivative of 1/(2sqrtx^2-6x+11)

The solution

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         1         
-------------------
       2           
    ___            
2*\/ x   - 6*x + 11

$$\frac{1}{\left(2 \left(\sqrt{x}\right)^{2} - 6 x\right) + 11}$$

1/(2*(sqrt(x))^2 - 6*x + 11)

Detail solution

Let $u = \left(2 \left(\sqrt{x}\right)^{2} - 6 x\right) + 11$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(2 \left(\sqrt{x}\right)^{2} - 6 x\right) + 11\right)$ :
1. Differentiate $\left(2 \left(\sqrt{x}\right)^{2} - 6 x\right) + 11$ term by term:
  1. Differentiate $2 \left(\sqrt{x}\right)^{2} - 6 x$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Let $u = \sqrt{x}$ .
      2. Apply the power rule: $u^{2}$ goes to $2 u$
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
        
        Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
        
        The result of the chain rule is:
        
        $1$
      So, the result is: $2$
    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: $-6$
    The result is: $-4$
  2. The derivative of the constant $11$ is zero.
  The result is: $-4$
The result of the chain rule is:

$\frac{4}{\left(\left(2 \left(\sqrt{x}\right)^{2} - 6 x\right) + 11\right)^{2}}$
Now simplify:

$\frac{4}{\left(11 - 4 x\right)^{2}}$

The answer is:

$\frac{4}{\left(11 - 4 x\right)^{2}}$

The graph

Plot the graph f(x)

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The first derivative [src]

          4           
----------------------
                     2
/       2           \ 
|    ___            | 
\2*\/ x   - 6*x + 11/

$$\frac{4}{\left(\left(2 \left(\sqrt{x}\right)^{2} - 6 x\right) + 11\right)^{2}}$$

Simplify

The second derivative [src]

     32    
-----------
          3
(11 - 4*x)

$$\frac{32}{\left(11 - 4 x\right)^{3}}$$

Simplify

The third derivative [src]

    384    
-----------
          4
(11 - 4*x)

$$\frac{384}{\left(11 - 4 x\right)^{4}}$$

Simplify