SOLUTION: If f(x)=8ln(6x+3ln(x)). Find f'(x)

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Question 1180593: If f(x)=8ln(6x+3ln(x)). Find f'(x)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If f%28x%29=8ln%286x%2B3ln%28x%29%29. Find f'%28x%29


%28d%2Fdx%29%288ln%286x%2B3ln%28x%29%29+%29...........take constant out

=8%28d%2Fdx%29%28ln%286x%2B3ln%28x%29%29+%29..........apply the chain rule

=%288%2F%286x%2B3ln%28x%29%29%29%2A%28d%2Fdx%29%2A%286x%2B3ln%28x%29%29

then %28d%2Fdx%29%286x%2B3ln%28x%29+%29=6%2B3%2Fx

=%288%2F%286x%2B3ln%28x%29%29%29%2A%286%2B3%2Fx%29.....simplify

=%288%2F%286x%2B3ln%28x%29%29%29%2A%28%286x%2B3%29%2Fx%29

=%288%2F%283%282x%2Bln%28x%29%29%29%29%2A%283%282x%2B1%29%2Fx%29

=%288%2F%28cross%283%29%282x%2Bln%28x%29%29%29%29%2A%28cross%283%29%282x%2B1%29%2Fx%29


=%288%282x%2B1%29%29%2F%28%282x%2Bln%28x%29%2Ax%29%29

=%2816x%2B8%29%2F%282x%5E2%2Bx%2Aln%28x%29%29

so,
f'%28x%29+=+%2816x+%2B+8%29%2F%282x%5E2+%2B+x%2Alog%28x%29%29