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Derivative of:
Derivative of (x^5+1)
Derivative of x^sqrt(x)
Derivative of log(x+2)
Derivative of ex^2
Identical expressions
fourteen *sqrt(two *x- three)
14 multiply by square root of (2 multiply by x minus 3)
fourteen multiply by square root of (two multiply by x minus three)
14*√(2*x-3)
14sqrt(2x-3)
14sqrt2x-3
Similar expressions
14*sqrt(2*x+3)

The derivative of the function/ 14*sqrt(2*x-3)

Derivative of 14sqrt(2x-3)

The solution

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     _________
14*\/ 2*x - 3

$$14 \sqrt{2 x - 3}$$

14*sqrt(2*x - 3)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
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 $-3$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $\frac{1}{\sqrt{2 x - 3}}$
So, the result is: $\frac{14}{\sqrt{2 x - 3}}$
Now simplify:

$\frac{14}{\sqrt{2 x - 3}}$

The answer is:

$\frac{14}{\sqrt{2 x - 3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     14    
-----------
  _________
\/ 2*x - 3

$$\frac{14}{\sqrt{2 x - 3}}$$

Simplify

The second derivative [src]

     -14     
-------------
          3/2
(-3 + 2*x)

$$- \frac{14}{\left(2 x - 3\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

      42     
-------------
          5/2
(-3 + 2*x)

$$\frac{42}{\left(2 x - 3\right)^{\frac{5}{2}}}$$

Simplify

The graph

Derivative of 14*sqrt(2*x-3)