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The derivative of the function/ (1-5x^(2/3))^10

Derivative of (1-5x^(2/3))^10

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
            10
/       2/3\  
\1 - 5*x   /
$$\left(1 - 5 x^{\frac{2}{3}}\right)^{10}$$ 
(1 - 5*x^(2/3))^10
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                 9
     /       2/3\ 
-100*\1 - 5*x   / 
------------------
       3 ___      
     3*\/ x
$$- \frac{100 \left(1 - 5 x^{\frac{2}{3}}\right)^{9}}{3 \sqrt[3]{x}}$$
Simplify
The second derivative [src] 
                 8 /             2/3\
    /        2/3\  |     -1 + 5*x   |
100*\-1 + 5*x   / *|10 - -----------|
                   |           2/3  |
                   \        9*x     /
-------------------------------------
                  2/3                
                 x
$$\frac{100 \left(10 - \frac{5 x^{\frac{2}{3}} - 1}{9 x^{\frac{2}{3}}}\right) \left(5 x^{\frac{2}{3}} - 1\right)^{8}}{x^{\frac{2}{3}}}$$
Simplify
The third derivative [src] 
                   /                                       2\
                 7 |        /        2/3\     /        2/3\ |
    /        2/3\  |400   5*\-1 + 5*x   /   2*\-1 + 5*x   / |
200*\-1 + 5*x   / *|--- - --------------- + ----------------|
                   |3*x          5/3                7/3     |
                   \            x               27*x        /
$$200 \left(5 x^{\frac{2}{3}} - 1\right)^{7} \left(\frac{400}{3 x} - \frac{5 \left(5 x^{\frac{2}{3}} - 1\right)}{x^{\frac{5}{3}}} + \frac{2 \left(5 x^{\frac{2}{3}} - 1\right)^{2}}{27 x^{\frac{7}{3}}}\right)$$
Simplify
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