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y=log3(2x+3)
The derivative of the function/ y=log3(2x+3)

Derivative of y=log3(2x+3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(2*x + 3)
------------
   log(3)
$$\frac{\log{\left(2 x + 3 \right)}}{\log{\left(3 \right)}}$$ 
d /log(2*x + 3)\
--|------------|
dx\   log(3)   /
$$\frac{d}{d x} \frac{\log{\left(2 x + 3 \right)}}{\log{\left(3 \right)}}$$
Transform
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] 
       2        
----------------
(2*x + 3)*log(3)
$$\frac{2}{\left(2 x + 3\right) \log{\left(3 \right)}}$$
Simplify
The second derivative [src] 
       -4        
-----------------
         2       
(3 + 2*x) *log(3)
$$- \frac{4}{\left(2 x + 3\right)^{2} \log{\left(3 \right)}}$$
Simplify
The third derivative [src] 
        16       
-----------------
         3       
(3 + 2*x) *log(3)
$$\frac{16}{\left(2 x + 3\right)^{3} \log{\left(3 \right)}}$$
Simplify
The graph
Derivative of y=log3(2x+3)
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