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3^3√x+2√x+1/2x^2
The derivative of the function/ 3^3√x+2√x+1/2x^2

Derivative of 3^3√x+2√x+1/2x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
                      2
 3   ___       ___   x 
3 *\/ x  + 2*\/ x  + --
                     2
$$2 \sqrt{x} + 3^{3} \sqrt{x} + \frac{x^{2}}{2}$$ 
  /                      2\
d | 3   ___       ___   x |
--|3 *\/ x  + 2*\/ x  + --|
dx\                     2 /
$$\frac{d}{d x} \left(2 \sqrt{x} + 3^{3} \sqrt{x} + \frac{x^{2}}{2}\right)$$
Transform
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:

    3. 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] 
       29  
x + -------
        ___
    2*\/ x
$$x + \frac{29}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
      29  
1 - ------
       3/2
    4*x
$$1 - \frac{29}{4 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
  87  
------
   5/2
8*x
$$\frac{87}{8 x^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of 3^3√x+2√x+1/2x^2
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