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

Derivative of ((√x-2^3)^4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
           4
/  ___    \ 
\\/ x  - 8/
$$\left(\sqrt{x} - 8\right)^{4}$$ 
(sqrt(x) - 8)^4
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. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      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] 
             3
  /  ___    \ 
2*\\/ x  - 8/ 
--------------
      ___     
    \/ x
$$\frac{2 \left(\sqrt{x} - 8\right)^{3}}{\sqrt{x}}$$
Simplify
The second derivative [src] 
            2 /           ___\
/       ___\  |3   -8 + \/ x |
\-8 + \/ x / *|- - ----------|
              |x       3/2   |
              \       x      /
$$\left(\frac{3}{x} - \frac{\sqrt{x} - 8}{x^{\frac{3}{2}}}\right) \left(\sqrt{x} - 8\right)^{2}$$
Simplify
The third derivative [src] 
               /                   2                 \
  /       ___\ |       /       ___\      /       ___\|
  |     \/ x | | 2     \-8 + \/ x /    3*\-8 + \/ x /|
3*|-4 + -----|*|---- + ------------- - --------------|
  \       2  / | 3/2         5/2              2      |
               \x           x                x       /
$$3 \left(\frac{\sqrt{x}}{2} - 4\right) \left(- \frac{3 \left(\sqrt{x} - 8\right)}{x^{2}} + \frac{2}{x^{\frac{3}{2}}} + \frac{\left(\sqrt{x} - 8\right)^{2}}{x^{\frac{5}{2}}}\right)$$
Simplify
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