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The derivative of the function/ log(x-3)

Derivative of log(x-3)

The solution

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log(x - 3)

\log{\left(x - 3 \right)}

log(x - 3)

Detail solution

Let $u = x - 3$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 3\right)$ :
1. Differentiate $x - 3$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $-3$ is zero.
  The result is: $1$
The result of the chain rule is:

$\frac{1}{x - 3}$
Now simplify:

$\frac{1}{x - 3}$

The answer is:

\frac{1}{x - 3}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1  
-----
x - 3

\frac{1}{x - 3}

Simplify

The second derivative [src]

   -1    
---------
        2
(-3 + x)

- \frac{1}{\left(x - 3\right)^{2}}

Simplify

The third derivative [src]

    2    
---------
        3
(-3 + x)

\frac{2}{\left(x - 3\right)^{3}}

Simplify

The graph

Derivative of log(x-3)