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

Derivative of -sqrt(2x+1)

The solution

You have entered [src]

   _________
-\/ 2*x + 1

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

-sqrt(2*x + 1)

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

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(2x+1)