Mister Exam

Other calculators

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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 .

    2. The derivative of is .

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

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        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] 
      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)
$$- \frac{1}{\left(x - 1\right)^{2} \log{\left(2 \right)}}$$
Simplify
The third derivative [src] 
       2        
----------------
        3       
(-1 + x) *log(2)
$$\frac{2}{\left(x - 1\right)^{3} \log{\left(2 \right)}}$$
Simplify
The graph
Derivative of y=log2(x-1)
    © Mister Exam – Calculator