Mister Exam

Other calculators

y=log6(9x+4)
The derivative of the function/ y=log6(9x+4)

Derivative of y=log6(9x+4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(9*x + 4)
------------
   log(6)
$$\frac{\log{\left(9 x + 4 \right)}}{\log{\left(6 \right)}}$$ 
log(9*x + 4)/log(6)
Detail solution

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

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. 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:

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       9        
----------------
(9*x + 4)*log(6)
$$\frac{9}{\left(9 x + 4\right) \log{\left(6 \right)}}$$
Simplify
The second derivative [src] 
       -81       
-----------------
         2       
(4 + 9*x) *log(6)
$$- \frac{81}{\left(9 x + 4\right)^{2} \log{\left(6 \right)}}$$
Simplify
The third derivative [src] 
       1458      
-----------------
         3       
(4 + 9*x) *log(6)
$$\frac{1458}{\left(9 x + 4\right)^{3} \log{\left(6 \right)}}$$
Simplify
The graph
Derivative of y=log6(9x+4)
    © Mister Exam – Calculator