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

Derivative of 2^3*sqrt(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    ___
8*\/ x
8x8 \sqrt{x} 
8*sqrt(x)
Detail solution

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

    1. Apply the power rule: x\sqrt{x} goes to 12x\frac{1}{2 \sqrt{x}}

    So, the result is: 4x\frac{4}{\sqrt{x}}

The answer is:

4x\frac{4}{\sqrt{x}}

The graph
02468-8-6-4-2-1010050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  4  
-----
  ___
\/ x
4x\frac{4}{\sqrt{x}}
Simplify
The second derivative [src] 
-2  
----
 3/2
x
−2x32- \frac{2}{x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
 3  
----
 5/2
x
3x52\frac{3}{x^{\frac{5}{2}}}
Simplify
The graph
Derivative of 2^3*sqrt(x)
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