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x/3+3/x
The derivative of the function/ x/3+3/x

Derivative of x/3+3/x

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

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The solution

You have entered [src] 
x   3
- + -
3   x
x3+3x\frac{x}{3} + \frac{3}{x} 
x/3 + 3/x
Detail solution

  1. Differentiate x3+3x\frac{x}{3} + \frac{3}{x} 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: 1x\frac{1}{x} goes to −1x2- \frac{1}{x^{2}}

      So, the result is: −3x2- \frac{3}{x^{2}}

    The result is: 13−3x2\frac{1}{3} - \frac{3}{x^{2}}

The answer is:

13−3x2\frac{1}{3} - \frac{3}{x^{2}}

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1   3 
- - --
3    2
    x
13−3x2\frac{1}{3} - \frac{3}{x^{2}}
Simplify
The second derivative [src] 
6 
--
 3
x
6x3\frac{6}{x^{3}}
Simplify
The third derivative [src] 
-18 
----
  4 
 x
−18x4- \frac{18}{x^{4}}
Simplify
The graph
Derivative of x/3+3/x
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