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Derivative of:
Derivative of (x^4+5)^cot(x)
Derivative of x^2*e^(3-2*x)*log(2)^x
Derivative of (x^2-8*x)/(x+1)
Derivative of x^2-4*x
Identical expressions
(- one)/sqrt(one - two *x)
( minus 1) divide by square root of (1 minus 2 multiply by x)
( minus 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)
-(1/sqrt(1-2x))

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

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sqrt{1 - 2 x}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. 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.
        
        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:
  
  $\frac{1}{\left(1 - 2 x\right)^{\frac{3}{2}}}$
So, the result 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      
------------
         3/2
(1 - 2*x)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify