Because f(x) contains the logarithm of a quotient, we'll
apply the quotient rule:
ln(f/g)=ln f -ln
g.
ln[(5x+7)/(5x+3)] = ln(5x+7) - ln
(5x+3)
f'(x) = [ln(5x+7) - ln
(5x+3)]'
f'(x) = [ln(5x+7)]' - [ln
(5x+3)]'
f'(x)= (5x+7)'/(5x+7) -
(5x+3)'/(5x+3)
f'(x) = 5/(5x+7) -
5/(5x+3)
We'll
factorize:
f'(x) = 5*[1/(5x+7) -
1/(5x+3)]
f'(x) =
5(5x+3-5x-7)/(5x+7)(5x+3)
f'(x) =
-20/(5x+7)(5x+3)
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