Find f'(x), f(x) = ((3x - 5) / (2x + 1))^3

Question

Find f'(x), f(x) = ((3x - 5) /  (2x + 1))^3

anonymous · Answer

for h(x) = f(x)/g(x) use the quotient rule [f'(x)g(x) - g'(x)f(x)]/g'(x)^2. Use the chain rule to evaluate g(x).

anonymous · Answer

I get up here:
$$3{{(3x - 5) \cdot 2 - (2x + 1) \cdot 3} \over (2x + 1)^2}^2$$

anonymous · Answer

ah sorry misread your function.... :/

anonymous · Answer

ahh, in the denominator is g'(x)^2 ? that's one of my mistakes

anonymous · Answer

this is a really good tutorial: http://tutorial.math.lamar.edu/Classes/CalcI/ProductQuotientRule.aspx

anonymous · Answer

ok.

anonymous · Answer

what's the answer? (-13 / (2x + 1))^3 ?

anonymous · Answer

or, 3(-13 / (2x + 1))^2

anonymous · Answer

well I haven't solved it all the way through, but I would simply it to $$(3x-5)^{3}/(2x+1)^{3}$$ then use the chain rule to find the derivatives of the numerator and denominator, then use the quotient rule to find the final answer.