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

Derivative of x^2-1/x+3

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

The graph:

from to

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The solution

You have entered [src] 
 2   1    
x  - - + 3
     x
(x2−1x)+3\left(x^{2} - \frac{1}{x}\right) + 3 
x^2 - 1/x + 3
Detail solution

  1. Differentiate (x2−1x)+3\left(x^{2} - \frac{1}{x}\right) + 3 term by term:

    1. Differentiate x2−1xx^{2} - \frac{1}{x} term by term:

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

      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: 1x2\frac{1}{x^{2}}

      The result is: 2x+1x22 x + \frac{1}{x^{2}}

    2. The derivative of the constant 33 is zero.

    The result is: 2x+1x22 x + \frac{1}{x^{2}}

The answer is:

2x+1x22 x + \frac{1}{x^{2}}

The graph
02468-8-6-4-2-1010200-100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1       
-- + 2*x
 2      
x
2x+1x22 x + \frac{1}{x^{2}}
Simplify
The second derivative [src] 
  /    1 \
2*|1 - --|
  |     3|
  \    x /
2(1−1x3)2 \left(1 - \frac{1}{x^{3}}\right)
Simplify
The third derivative [src] 
6 
--
 4
x
6x4\frac{6}{x^{4}}
Simplify
The graph
Derivative of x^2-1/x+3
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