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

Derivative of sqrt(1-2x)

The solution

You have entered [src]

  _________
\/ 1 - 2*x

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

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

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

Transform

Detail solution

Let $u = 1 - 2 x$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
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. 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: $2$
    So, the result is: $-2$
  The result is: $-2$
The result of the chain rule is:

$- \frac{1}{\sqrt{1 - 2 x}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of sqrt(1-2x)