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Derivative of:
Derivative of e^(5*x)
Derivative of x^2+x+1
Derivative of (x^2+1)^2
Derivative of sqrt(2*x)
Identical expressions
one / three *x³+ one /2lnx
1 divide by 3 multiply by x³ plus 1 divide by 2lnx
one divide by three multiply by x³ plus one divide by 2lnx
1/3x³+1/2lnx
1 divide by 3*x³+1 divide by 2lnx
Similar expressions
1/3*x³-1/2lnx

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

Derivative of 1/3*x³+1/2lnx

The solution

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 3         
x    log(x)
-- + ------
3      2

$$\frac{x^{3}}{3} + \frac{\log{\left(x \right)}}{2}$$

x^3/3 + log(x)/2

Detail solution

Differentiate $\frac{x^{3}}{3} + \frac{\log{\left(x \right)}}{2}$ 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: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  So, the result is: $\frac{1}{2 x}$
The result is: $x^{2} + \frac{1}{2 x}$
Now simplify:

$\frac{x^{3} + \frac{1}{2}}{x}$

The answer is:

$\frac{x^{3} + \frac{1}{2}}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2    1 
x  + ---
     2*x

$$x^{2} + \frac{1}{2 x}$$

Simplify

The second derivative [src]

       1  
2*x - ----
         2
      2*x

$$2 x - \frac{1}{2 x^{2}}$$

Simplify

The third derivative [src]

$$2 + \frac{1}{x^{3}}$$

Simplify