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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

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The solution

You have entered [src] 
     2          
x   x      _____
- + -- + \/ 4*x 
3   2
4x+x22+x3\sqrt{4 x} + \frac{x^{2}}{2} + \frac{x}{3} 
  /     2          \
d |x   x      _____|
--|- + -- + \/ 4*x |
dx\3   2           /
ddx(4x+x22+x3)\frac{d}{d x} \left(\sqrt{4 x} + \frac{x^{2}}{2} + \frac{x}{3}\right)
Transform
Detail solution

  1. Differentiate 4x+x22+x3\sqrt{4 x} + \frac{x^{2}}{2} + \frac{x}{3} 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: xx goes to 11

      So, the result is: 13\frac{1}{3}

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

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      So, the result is: xx

    3. Let u=4xu = 4 x.

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

    5. Then, apply the chain rule. Multiply by ddx4x\frac{d}{d x} 4 x:

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

        1. Apply the power rule: xx goes to 11

        So, the result is: 44

      The result of the chain rule is:

      1x\frac{1}{\sqrt{x}}

    The result is: x+13+1xx + \frac{1}{3} + \frac{1}{\sqrt{x}}

The answer is:

x+13+1xx + \frac{1}{3} + \frac{1}{\sqrt{x}}

The graph
02468-8-6-4-2-10100100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            ___
1       2*\/ x 
- + x + -------
3         2*x
2x2x+x+13\frac{2 \sqrt{x}}{2 x} + x + \frac{1}{3}
Simplify
The second derivative [src] 
      1   
1 - ------
       3/2
    2*x
1−12x321 - \frac{1}{2 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
  3   
------
   5/2
4*x
34x52\frac{3}{4 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of 1/3x+1/2x^2+√4x
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