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1/3x+1/2x^2+√4x
The derivative of the function/ 1/3x+1/2x^2+√4x

Derivative of 1/3x+1/2x^2+√4x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     2          
x   x      _____
- + -- + \/ 4*x 
3   2
$$\sqrt{4 x} + \frac{x^{2}}{2} + \frac{x}{3}$$ 
  /     2          \
d |x   x      _____|
--|- + -- + \/ 4*x |
dx\3   2           /
$$\frac{d}{d x} \left(\sqrt{4 x} + \frac{x^{2}}{2} + \frac{x}{3}\right)$$
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. Let .

    4. Apply the power rule: goes to

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

      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:

      The result of the chain rule is:

    The result is:

The answer is:

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