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The derivative of the function/ 1/3*x³+1/2lnx

Derivative of 1/3*x³+1/2lnx

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

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The solution

You have entered [src] 
 3         
x    log(x)
-- + ------
3      2
x33+log⁡(x)2\frac{x^{3}}{3} + \frac{\log{\left(x \right)}}{2} 
x^3/3 + log(x)/2
Detail solution

  1. Differentiate x33+log⁡(x)2\frac{x^{3}}{3} + \frac{\log{\left(x \right)}}{2} 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: x3x^{3} goes to 3x23 x^{2}

      So, the result is: x2x^{2}

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

      1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

      So, the result is: 12x\frac{1}{2 x}

    The result is: x2+12xx^{2} + \frac{1}{2 x}

  2. Now simplify:

    x3+12x\frac{x^{3} + \frac{1}{2}}{x}

The answer is:

x3+12x\frac{x^{3} + \frac{1}{2}}{x}

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 2    1 
x  + ---
     2*x
x2+12xx^{2} + \frac{1}{2 x}
Simplify
The second derivative [src] 
       1  
2*x - ----
         2
      2*x
2x−12x22 x - \frac{1}{2 x^{2}}
Simplify
The third derivative [src] 
    1 
2 + --
     3
    x
2+1x32 + \frac{1}{x^{3}}
Simplify
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