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Derivative of:
Derivative of x^-5-4*x^-3+2*x-3
Derivative of sin(x)/x^5
Derivative of 3*x^4+cos(5*x)
Derivative of -2/3*x
Identical expressions
cbrt(x- one)^ two
cubic root of (x minus 1) squared
cubic root of (x minus one) to the power of two
cbrt(x-1)2
cbrtx-12
cbrt(x-1)²
cbrt(x-1) to the power of 2
cbrtx-1^2
Similar expressions
cbrt(x+1)^2

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

Derivative of cbrt(x-1)^2

The solution

You have entered [src]

         2
3 _______ 
\/ x - 1

$$\left(\sqrt[3]{x - 1}\right)^{2}$$

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

Detail solution

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

$\frac{2}{3 \sqrt[3]{x - 1}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$\frac{2 \left(x - 1\right)^{\frac{2}{3}}}{3 \left(x - 1\right)}$$

Simplify

The second derivative [src]

     -2      
-------------
          4/3
9*(-1 + x)

$$- \frac{2}{9 \left(x - 1\right)^{\frac{4}{3}}}$$

Simplify

The third derivative [src]

      8       
--------------
           7/3
27*(-1 + x)

$$\frac{8}{27 \left(x - 1\right)^{\frac{7}{3}}}$$

Simplify