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The derivative of the function/ y=sqrt(2x-3)+2

Derivative of y=sqrt(2x-3)+2

The solution

You have entered [src]

  _________    
\/ 2*x - 3  + 2

$$\sqrt{2 x - 3} + 2$$

d /  _________    \
--\\/ 2*x - 3  + 2/
dx

$$\frac{d}{d x} \left(\sqrt{2 x - 3} + 2\right)$$

Transform

Detail solution

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

$\frac{1}{\sqrt{2 x - 3}}$

The answer is:

$\frac{1}{\sqrt{2 x - 3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     1     
-----------
  _________
\/ 2*x - 3

$$\frac{1}{\sqrt{2 x - 3}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of y=sqrt(2x-3)+2