Mister Exam

Derivative of x/(3*x+5)

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

The graph:

from to

Piecewise:

The solution

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

    and .

    To find :

    1. Apply the power rule: goes to

    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]
   1         3*x    
------- - ----------
3*x + 5            2
          (3*x + 5) 
$$- \frac{3 x}{\left(3 x + 5\right)^{2}} + \frac{1}{3 x + 5}$$
The second derivative [src]
  /       3*x  \
6*|-1 + -------|
  \     5 + 3*x/
----------------
            2   
   (5 + 3*x)    
$$\frac{6 \left(\frac{3 x}{3 x + 5} - 1\right)}{\left(3 x + 5\right)^{2}}$$
The third derivative [src]
   /      3*x  \
54*|1 - -------|
   \    5 + 3*x/
----------------
            3   
   (5 + 3*x)    
$$\frac{54 \left(- \frac{3 x}{3 x + 5} + 1\right)}{\left(3 x + 5\right)^{3}}$$