Answer
$\frac{dy}{dt}$ = $\frac{-130(5t+2)^{4}}{(3t-4)^{6}}$
Work Step by Step
$y$ = $(\frac{3t-4}{5t+2})^{-5}$
$\frac{dy}{dt}$ = $(-5)(\frac{3t-4}{5t+2})^{-6}$ $\frac{d}{dt}$$(\frac{3t-4}{5t+2})$
$\frac{dy}{dt}$ = $(-5)(\frac{3t-4}{5t+2})^{-6}$ [$\frac{(5t+2)\frac{d}{dt}(3t-4) - (3t-4)\frac{d}{dt}(5t+2)}{(5t+2)^{2}}$]
$\frac{dy}{dt}$ = $(-5)(\frac{3t-4}{5t+2})^{-6}$ [$\frac{(5t+2)(3) - (3t-4)(5)}{(5t+2)^{2}}$]
$\frac{dy}{dt}$ = $(-5)(\frac{3t-4}{5t+2})^{-6}$ [$\frac{15t+6-15t+20}{(5t+2)^{2}}$]
$\frac{dy}{dt}$ = $(-5)(\frac{3t-4}{5t+2})^{-6}$ [$\frac{26}{(5t+2)^{2}}$]
$\frac{dy}{dt}$ = $(-5)\frac{(5t+2)^{6}}{(3t-4)^{6}}$ [$\frac{26}{(5t+2)^{2}}$]
$\frac{dy}{dt}$ = $\frac{-130(5t+2)^{4}}{(3t-4)^{6}}$
