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)#