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Identical expressions
x^ two - one /x+ three
x squared minus 1 divide by x plus 3
x to the power of two minus one divide by x plus three
x2-1/x+3
x²-1/x+3
x to the power of 2-1/x+3
x^2-1 divide by x+3
Similar expressions
x^2-1/x-3
x^2+1/x+3
(x^2-1)/(x+3)

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

Derivative of x^2-1/x+3

The solution

You have entered [src]

 2   1    
x  - - + 3
     x

$$\left(x^{2} - \frac{1}{x}\right) + 3$$

x^2 - 1/x + 3

Detail solution

Differentiate $\left(x^{2} - \frac{1}{x}\right) + 3$ term by term:
1. Differentiate $x^{2} - \frac{1}{x}$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
    So, the result is: $\frac{1}{x^{2}}$
  The result is: $2 x + \frac{1}{x^{2}}$
2. The derivative of the constant $3$ is zero.
The result is: $2 x + \frac{1}{x^{2}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1       
-- + 2*x
 2      
x

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

Simplify

The second derivative [src]

  /    1 \
2*|1 - --|
  |     3|
  \    x /

$$2 \left(1 - \frac{1}{x^{3}}\right)$$

Simplify

The third derivative [src]

6 
--
 4
x

$$\frac{6}{x^{4}}$$

Simplify

The graph

Derivative of x^2-1/x+3