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y=log2(x-1)
The derivative of the function/ y=log2(x-1)

Derivative of y=log2(x-1)

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

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The solution

You have entered [src] 
log(x - 1)
----------
  log(2)
log⁡(x−1)log⁡(2)\frac{\log{\left(x - 1 \right)}}{\log{\left(2 \right)}} 
log(x - 1)/log(2)
Detail solution

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

    1. Let u=x−1u = x - 1.

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

    3. Then, apply the chain rule. Multiply by ddx(x−1)\frac{d}{d x} \left(x - 1\right):

      1. Differentiate x−1x - 1 term by term:

        1. Apply the power rule: xx goes to 11

        2. The derivative of the constant −1-1 is zero.

        The result is: 11

      The result of the chain rule is:

      1x−1\frac{1}{x - 1}

    So, the result is: 1(x−1)log⁡(2)\frac{1}{\left(x - 1\right) \log{\left(2 \right)}}

  2. Now simplify:

    1(x−1)log⁡(2)\frac{1}{\left(x - 1\right) \log{\left(2 \right)}}

The answer is:

1(x−1)log⁡(2)\frac{1}{\left(x - 1\right) \log{\left(2 \right)}}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      1       
--------------
(x - 1)*log(2)
1(x−1)log⁡(2)\frac{1}{\left(x - 1\right) \log{\left(2 \right)}}
Simplify
The second derivative [src] 
      -1        
----------------
        2       
(-1 + x) *log(2)
−1(x−1)2log⁡(2)- \frac{1}{\left(x - 1\right)^{2} \log{\left(2 \right)}}
Simplify
The third derivative [src] 
       2        
----------------
        3       
(-1 + x) *log(2)
2(x−1)3log⁡(2)\frac{2}{\left(x - 1\right)^{3} \log{\left(2 \right)}}
Simplify
The graph
Derivative of y=log2(x-1)
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