How do you differentiate $f(x)= 5ln(x-2)^3$ ?

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Answer 1 · 2017-08-22T14:47:58

The derivative is $=15/(x-2)$

We need

$(x^n)'=nx^(n-1)$

$(lnx)'=1/x$

The derivative of $f(x)=aln u(x)$ is

$f'(x)=a/(u(x))*u'(x)$

Here, we have

$f(x)=5ln(x-2)^3$ , $<=>$ , $f(x)=15ln(x-2)$

There are 2 ways of calculating the derivative

Therefore,

$f'(x)=5/(x-2)^3*3(x-2)^2=15/(x-2)$

or

$f'(x)=(15ln(x-2))'=15/(x-2)$

How do you differentiate f(x)= 5ln(x-2)^3f(x)= 5ln(x-2)^3?