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

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Derivative of:
Derivative of x^(4/5)
Derivative of x^2+5
Derivative of x^3-1/5*x^2+2*x-4
Derivative of |x-1|
Identical expressions
-(one /sqrt(one -2x))
minus (1 divide by square root of (1 minus 2x))
minus (one divide by square root of (one minus 2x))
-(1/√(1-2x))
-1/sqrt1-2x
-(1 divide by sqrt(1-2x))
Similar expressions
-(1/sqrt(1+2x))
(1/sqrt(1-2x))

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

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

The solution

You have entered [src]

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

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

d /    -1     \
--|-----------|
dx|  _________|
  \\/ 1 - 2*x /

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

Transform

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.
        
        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: $2$
        
        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: $- \frac{1}{\left(1 - 2 x\right)^{\frac{3}{2}}}$
Now simplify:

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

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

The graph

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