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log(x-2)
The derivative of the function/ log(x-2)

Derivative of log(x-2)

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

The graph:

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Piecewise:

The solution

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

  1. Let u=x−2u = x - 2.

  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−2)\frac{d}{d x} \left(x - 2\right):

    1. Differentiate x−2x - 2 term by term:

      1. Apply the power rule: xx goes to 11

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

      The result is: 11

    The result of the chain rule is:

    1x−2\frac{1}{x - 2}

  4. Now simplify:

    1x−2\frac{1}{x - 2}

The answer is:

1x−2\frac{1}{x - 2}

The graph
02468-8-6-4-2-1010-2525
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1  
-----
x - 2
1x−2\frac{1}{x - 2}
Simplify
The second derivative [src] 
   -1    
---------
        2
(-2 + x)
−1(x−2)2- \frac{1}{\left(x - 2\right)^{2}}
Simplify
The third derivative [src] 
    2    
---------
        3
(-2 + x)
2(x−2)3\frac{2}{\left(x - 2\right)^{3}}
Simplify
The graph
Derivative of log(x-2)
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