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Derivative of f(x)=(-3x+5)/(2x-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 
$$\frac{5 - 3 x}{2 x - 1}$$
(-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)  
$$- \frac{2 \left(5 - 3 x\right)}{\left(2 x - 1\right)^{2}} - \frac{3}{2 x - 1}$$
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)       
$$\frac{24 \left(-3 + \frac{2 \left(3 x - 5\right)}{2 x - 1}\right)}{\left(2 x - 1\right)^{3}}$$