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Derivative of:
Derivative of (x^2+1)/x
Derivative of coth(x)/tanh(x)
Derivative of x/sin(x)
Derivative of x^3-3*x^2
Integral of d{x}:
(x^2+1)/x
Graphing y =:
(x^2+1)/x
Identical expressions
(x^ two + one)/x
(x squared plus 1) divide by x
(x to the power of two plus one) divide by x
(x2+1)/x
x2+1/x
(x²+1)/x
(x to the power of 2+1)/x
x^2+1/x
(x^2+1) divide by x
Similar expressions
4*x^2+1/x^4-1/x
(x^4+x^2+1)/(x+1)
(x^2+1)/(x-1)
(x^2+1)/(x-2)
(x^2-1)/x

The derivative of the function/ (x^2+1)/x

Derivative of (x^2+1)/x

The solution

You have entered [src]

 2    
x  + 1
------
  x

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

(x^2 + 1)/x

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2} + 1$ and $g{\left(x \right)} = x$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
Now plug in to the quotient rule:

$\frac{x^{2} - 1}{x^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /         2\
  |    1 + x |
6*|1 - ------|
  |       2  |
  \      x   /
--------------
       2      
      x

$$\frac{6 \left(1 - \frac{x^{2} + 1}{x^{2}}\right)}{x^{2}}$$

Simplify

The graph

Derivative of (x^2+1)/x