Question

find the derivative of the following function.
y = (5t - 1)(2t - 2)^(-1)
\frac{dy}{dt}=\square

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}$. Here, $u = 5t - 1$, $v=(2t - 2)$, $u^\prime=5$, and $v^\prime = 2$.

Step2: Substitute values into quotient - rule formula

$\frac{dy}{dt}=\frac{5(2t - 2)-(5t - 1)\times2}{(2t - 2)^{2}}$.

Step3: Expand the numerator

First, expand $5(2t - 2)=10t-10$ and $(5t - 1)\times2 = 10t-2$. Then the numerator is $(10t - 10)-(10t - 2)=10t-10 - 10t + 2=-8$.

Answer:

$\frac{-8}{(2t - 2)^{2}}$