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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

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The solution

You have entered [src] 
log(2*x + 3)
------------
   log(3)
log⁡(2x+3)log⁡(3)\frac{\log{\left(2 x + 3 \right)}}{\log{\left(3 \right)}} 
d /log(2*x + 3)\
--|------------|
dx\   log(3)   /
ddxlog⁡(2x+3)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 u=2x+3u = 2 x + 3.

    2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

    3. Then, apply the chain rule. Multiply by ddx(2x+3)\frac{d}{d x} \left(2 x + 3\right):

      1. Differentiate 2x+32 x + 3 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: xx goes to 11

          So, the result is: 22

        2. The derivative of the constant 33 is zero.

        The result is: 22

      The result of the chain rule is:

      22x+3\frac{2}{2 x + 3}

    So, the result is: 2(2x+3)log⁡(3)\frac{2}{\left(2 x + 3\right) \log{\left(3 \right)}}

  2. Now simplify:

    2(2x+3)log⁡(3)\frac{2}{\left(2 x + 3\right) \log{\left(3 \right)}}

The answer is:

2(2x+3)log⁡(3)\frac{2}{\left(2 x + 3\right) \log{\left(3 \right)}}

The graph
02468-8-6-4-2-1010-10050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       2        
----------------
(2*x + 3)*log(3)
2(2x+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)
−4(2x+3)2log⁡(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)
16(2x+3)3log⁡(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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