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(3*x+5)/(2*x-1)

Derivative of (3*x+5)/(2*x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3*x + 5
-------
2*x - 1
$$\frac{3 x + 5}{2 x - 1}$$
(3*x + 5)/(2*x - 1)
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. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    Now plug in to the quotient rule:


The answer is:

The graph
The first derivative [src]
   3      2*(3*x + 5)
------- - -----------
2*x - 1             2
           (2*x - 1) 
$$\frac{3}{2 x - 1} - \frac{2 \left(3 x + 5\right)}{\left(2 x - 1\right)^{2}}$$
The second derivative [src]
  /     2*(5 + 3*x)\
4*|-3 + -----------|
  \       -1 + 2*x /
--------------------
              2     
    (-1 + 2*x)      
$$\frac{4 \left(-3 + \frac{2 \left(3 x + 5\right)}{2 x - 1}\right)}{\left(2 x - 1\right)^{2}}$$
The third derivative [src]
   /    2*(5 + 3*x)\
24*|3 - -----------|
   \      -1 + 2*x /
--------------------
              3     
    (-1 + 2*x)      
$$\frac{24 \left(3 - \frac{2 \left(3 x + 5\right)}{2 x - 1}\right)}{\left(2 x - 1\right)^{3}}$$
The graph
Derivative of (3*x+5)/(2*x-1)