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Derivative of:
Derivative of x^(sin(x)^(2))
Derivative of x^3-6*x^2
Derivative of x^3-5x^2+x
Derivative of (x+3)^2(x+5)-1
Identical expressions
three / two sqrt(3x+2)
3 divide by 2 square root of (3x plus 2)
three divide by two square root of (3x plus 2)
3/2√(3x+2)
3/2sqrt3x+2
3 divide by 2sqrt(3x+2)
Similar expressions
3/2sqrt(3x-2)

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

Derivative of 3/2sqrt(3x+2)

The solution

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

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

3*sqrt(3*x + 2)/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 x + 2$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + 2\right)$ :
  1. Differentiate $3 x + 2$ 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: $3$
    2. The derivative of the constant $2$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $\frac{3}{2 \sqrt{3 x + 2}}$
So, the result is: $\frac{9}{4 \sqrt{3 x + 2}}$
Now simplify:

$\frac{9}{4 \sqrt{3 x + 2}}$

The answer is:

$\frac{9}{4 \sqrt{3 x + 2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      9      
-------------
    _________
4*\/ 3*x + 2

$$\frac{9}{4 \sqrt{3 x + 2}}$$

Simplify

The second derivative [src]

     -27      
--------------
           3/2
8*(2 + 3*x)

$$- \frac{27}{8 \left(3 x + 2\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

      243      
---------------
            5/2
16*(2 + 3*x)

$$\frac{243}{16 \left(3 x + 2\right)^{\frac{5}{2}}}$$

Simplify