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

Derivative of y=sqrt(2x-3)

The solution

You have entered [src]

  _________
\/ 2*x - 3

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

sqrt(2*x - 3)

Detail solution

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