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Derivative of:
Derivative of (sin(x))^2
Derivative of x-1
Derivative of sin(x)+cos(x)
Derivative of asin(x)
Identical expressions
one /(2x- four)^ one / three
1 divide by (2x minus 4) to the power of 1 divide by 3
one divide by (2x minus four) to the power of one divide by three
1/(2x-4)1/3
1/2x-41/3
1/2x-4^1/3
1 divide by (2x-4)^1 divide by 3
Similar expressions
1/(2x+4)^1/3

The derivative of the function/ 1/(2x-4)^1/3

Derivative of 1/(2x-4)^1/3

The solution

You have entered [src]

     1     
-----------
3 _________
\/ 2*x - 4

$$\frac{1}{\sqrt[3]{2 x - 4}}$$

1/((2*x - 4)^(1/3))

Detail solution

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

$- \frac{2}{3 \left(2 x - 4\right)^{\frac{4}{3}}}$
Now simplify:

$- \frac{2^{\frac{2}{3}}}{6 \left(x - 2\right)^{\frac{4}{3}}}$

The answer is:

$- \frac{2^{\frac{2}{3}}}{6 \left(x - 2\right)^{\frac{4}{3}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$- \frac{2}{3 \sqrt[3]{2 x - 4} \left(2 x - 4\right)}$$

Simplify

The second derivative [src]

       2/3   
    2*2      
-------------
          7/3
9*(-2 + x)

$$\frac{2 \cdot 2^{\frac{2}{3}}}{9 \left(x - 2\right)^{\frac{7}{3}}}$$

Simplify

The third derivative [src]

         2/3   
    -14*2      
---------------
           10/3
27*(-2 + x)

$$- \frac{14 \cdot 2^{\frac{2}{3}}}{27 \left(x - 2\right)^{\frac{10}{3}}}$$

Simplify