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Derivative of (5-4*x)/(3*x+5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
5 - 4*x
-------
3*x + 5
$$\frac{5 - 4 x}{3 x + 5}$$
(5 - 4*x)/(3*x + 5)
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]
     4      3*(5 - 4*x)
- ------- - -----------
  3*x + 5             2
             (3*x + 5) 
$$- \frac{3 \left(5 - 4 x\right)}{\left(3 x + 5\right)^{2}} - \frac{4}{3 x + 5}$$
The second derivative [src]
  /    3*(-5 + 4*x)\
6*|4 - ------------|
  \      5 + 3*x   /
--------------------
              2     
     (5 + 3*x)      
$$\frac{6 \left(4 - \frac{3 \left(4 x - 5\right)}{3 x + 5}\right)}{\left(3 x + 5\right)^{2}}$$
The third derivative [src]
   /     3*(-5 + 4*x)\
54*|-4 + ------------|
   \       5 + 3*x   /
----------------------
               3      
      (5 + 3*x)       
$$\frac{54 \left(-4 + \frac{3 \left(4 x - 5\right)}{3 x + 5}\right)}{\left(3 x + 5\right)^{3}}$$