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16*sqrt(x)-4*x^2
The derivative of the function/ 16*sqrt(x)-4*x^2

Derivative of 16*sqrt(x)-4*x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     ___      2
16*\/ x  - 4*x
$$16 \sqrt{x} - 4 x^{2}$$ 
16*sqrt(x) - 4*x^2
Detail solution

  1. Differentiate 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: goes to

      So, the result is:

    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 answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
         8  
-8*x + -----
         ___
       \/ x
$$- 8 x + \frac{8}{\sqrt{x}}$$
Simplify
The second derivative [src] 
   /     1  \
-4*|2 + ----|
   |     3/2|
   \    x   /
$$- 4 \left(2 + \frac{1}{x^{\frac{3}{2}}}\right)$$
Simplify
The third derivative [src] 
 6  
----
 5/2
x
$$\frac{6}{x^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of 16*sqrt(x)-4*x^2
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