find the derivative of the following function.\ny = (5t - 1)(2t - 2)^(-1)\n\\frac{dy}{dt}=\\square
find the derivative of the following function.\ny = (5t - 1)(2t - 2)^(-1)\n\\frac{dy}{dt}=\\square
Answer
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:
$\frac{-8}{(2t - 2)^{2}}$