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Derivative of:
Derivative of sqrt(cos(x))
Derivative of cos(2t)
Derivative of 5*tan(x)
Derivative of 3xsinx
Identical expressions
(- four)/sqrt(three *x- two)
( minus 4) divide by square root of (3 multiply by x minus 2)
( minus four) divide by square root of (three multiply by x minus two)
(-4)/√(3*x-2)
(-4)/sqrt(3x-2)
-4/sqrt3x-2
(-4) divide by sqrt(3*x-2)
Similar expressions
(-4)/sqrt(3*x+2)
(4)/sqrt(3*x-2)

The derivative of the function/ (-4)/sqrt(3*x-2)

Derivative of (-4)/sqrt(3*x-2)

The solution

You have entered [src]

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

$$- \frac{4}{\sqrt{3 x - 2}}$$

-4/sqrt(3*x - 2)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sqrt{3 x - 2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{3 x - 2}$ :
  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.
        
        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:
    
    $\frac{3}{2 \sqrt{3 x - 2}}$
  The result of the chain rule is:
  
  $- \frac{3}{2 \left(3 x - 2\right)^{\frac{3}{2}}}$
So, the result is: $\frac{6}{\left(3 x - 2\right)^{\frac{3}{2}}}$
Now simplify:

$\frac{6}{\left(3 x - 2\right)^{\frac{3}{2}}}$

The answer is:

$\frac{6}{\left(3 x - 2\right)^{\frac{3}{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     6      
------------
         3/2
(3*x - 2)

$$\frac{6}{\left(3 x - 2\right)^{\frac{3}{2}}}$$

Simplify

The second derivative [src]

     -27     
-------------
          5/2
(-2 + 3*x)

$$- \frac{27}{\left(3 x - 2\right)^{\frac{5}{2}}}$$

Simplify

The third derivative [src]

      405      
---------------
            7/2
2*(-2 + 3*x)

$$\frac{405}{2 \left(3 x - 2\right)^{\frac{7}{2}}}$$

Simplify