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Derivative of:
Derivative of e^-1
Derivative of 2*x^5
Derivative of sin(2*x^2+3)
Derivative of f(x)=5
Identical expressions
one /sqrt(ten *x- ten)
1 divide by square root of (10 multiply by x minus 10)
one divide by square root of (ten multiply by x minus ten)
1/√(10*x-10)
1/sqrt(10x-10)
1/sqrt10x-10
1 divide by sqrt(10*x-10)
Similar expressions
1/sqrt(10*x+10)

The derivative of the function/ 1/sqrt(10*x-10)

Derivative of 1/sqrt(10*x-10)

The solution

You have entered [src]

      1      
-------------
  ___________
\/ 10*x - 10

$$\frac{1}{\sqrt{10 x - 10}}$$

1/(sqrt(10*x - 10))

Detail solution

Let $u = \sqrt{10 x - 10}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{10 x - 10}$ :
1. Let $u = 10 x - 10$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(10 x - 10\right)$ :
  1. Differentiate $10 x - 10$ term by term:
    1. 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: $10$
    2. The derivative of the constant $-10$ is zero.
    The result is: $10$
  The result of the chain rule is:
  
  $\frac{5}{\sqrt{10 x - 10}}$
The result of the chain rule is:

$- \frac{5}{\left(10 x - 10\right)^{\frac{3}{2}}}$
Now simplify:

$- \frac{\sqrt{10}}{20 \left(x - 1\right)^{\frac{3}{2}}}$

The answer is:

$- \frac{\sqrt{10}}{20 \left(x - 1\right)^{\frac{3}{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           -5            
-------------------------
              ___________
(10*x - 10)*\/ 10*x - 10

$$- \frac{5}{\sqrt{10 x - 10} \left(10 x - 10\right)}$$

Simplify

The second derivative [src]

       ____   
   3*\/ 10    
--------------
           5/2
40*(-1 + x)

$$\frac{3 \sqrt{10}}{40 \left(x - 1\right)^{\frac{5}{2}}}$$

Simplify

The third derivative [src]

       ____   
  -3*\/ 10    
--------------
           7/2
16*(-1 + x)

$$- \frac{3 \sqrt{10}}{16 \left(x - 1\right)^{\frac{7}{2}}}$$

Simplify