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Derivative of:
Derivative of x^-6
Derivative of f(x)=1
Derivative of e^x*x^2
Derivative of 2*sqrt(x^3)
Identical expressions
one /sqrt(one - two *x)
1 divide by square root of (1 minus 2 multiply by x)
one divide by square root of (one minus two multiply by x)
1/√(1-2*x)
1/sqrt(1-2x)
1/sqrt1-2x
1 divide by sqrt(1-2*x)
Similar expressions
1/sqrt(1+2*x)
1/(sqrt(1-2*x))

The derivative of the function/ 1/sqrt(1-2*x)

Derivative of 1/sqrt(1-2*x)

The solution

You have entered [src]

     1     
-----------
  _________
\/ 1 - 2*x

$$\frac{1}{\sqrt{1 - 2 x}}$$

1/(sqrt(1 - 2*x))

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          1          
---------------------
            _________
(1 - 2*x)*\/ 1 - 2*x

$$\frac{1}{\sqrt{1 - 2 x} \left(1 - 2 x\right)}$$

Simplify

The second derivative [src]

     3      
------------
         5/2
(1 - 2*x)

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

Simplify

4-я производная [src]

    105     
------------
         9/2
(1 - 2*x)

$$\frac{105}{\left(1 - 2 x\right)^{\frac{9}{2}}}$$

Simplify

The third derivative [src]

     15     
------------
         7/2
(1 - 2*x)

$$\frac{15}{\left(1 - 2 x\right)^{\frac{7}{2}}}$$

Simplify