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Derivative of (x^2+5)/(x-3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2    
x  + 5
------
x - 3 
$$\frac{x^{2} + 5}{x - 3}$$
(x^2 + 5)/(x - 3)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:


The answer is:

The graph
The first derivative [src]
    2             
   x  + 5     2*x 
- -------- + -----
         2   x - 3
  (x - 3)         
$$\frac{2 x}{x - 3} - \frac{x^{2} + 5}{\left(x - 3\right)^{2}}$$
The second derivative [src]
  /           2          \
  |      5 + x      2*x  |
2*|1 + --------- - ------|
  |            2   -3 + x|
  \    (-3 + x)          /
--------------------------
          -3 + x          
$$\frac{2 \left(- \frac{2 x}{x - 3} + 1 + \frac{x^{2} + 5}{\left(x - 3\right)^{2}}\right)}{x - 3}$$
3-я производная [src]
  /            2          \
  |       5 + x      2*x  |
6*|-1 - --------- + ------|
  |             2   -3 + x|
  \     (-3 + x)          /
---------------------------
                 2         
         (-3 + x)          
$$\frac{6 \left(\frac{2 x}{x - 3} - 1 - \frac{x^{2} + 5}{\left(x - 3\right)^{2}}\right)}{\left(x - 3\right)^{2}}$$
The third derivative [src]
  /            2          \
  |       5 + x      2*x  |
6*|-1 - --------- + ------|
  |             2   -3 + x|
  \     (-3 + x)          /
---------------------------
                 2         
         (-3 + x)          
$$\frac{6 \left(\frac{2 x}{x - 3} - 1 - \frac{x^{2} + 5}{\left(x - 3\right)^{2}}\right)}{\left(x - 3\right)^{2}}$$