Answer
$\frac{-130(5t+2)^4}{(3t-4)^6}$
Work Step by Step
y=$(\frac{3t-4}{5t+2})^{-5}$
Apply the chain rule:
$\frac{dy}{dt}=-5(\frac{3t-4}{5t+2})^{-6}.\frac{(5t+2).3-(3t-4).5}{(5t+2)^2}$
=-5$(\frac{5t+2}{3t-4})^6.\frac{15t+6-15t+20}{(5t+2)^2}$
=$-5\frac{(5t+2)^6}{(3t-4)^6}.\frac{26}{(5t+2)^2}$
=$\frac{-130(5t+2)^4}{(3t-4)^6}$
