Answered: "Derivatives Find and simplify the derivative of the..." - Plainmath

angepepagiortzb

Answered question

2021-11-26

Derivatives Find and simplify the derivative of the following functions.

y = (3 t - 1) {(2 t - 2)}^{- 1}

Answer & Explanation

Wasither1957

Beginner2021-11-27Added 17 answers

Given,

y = (3 t - 1) {(2 t - 2)}^{- 1}

\Rightarrow y = \frac{3 t - 1}{2 t - 2}

Differentiating with respect to t, we get

\Rightarrow \frac{d y}{d t} = \frac{\frac{d (3 t - 1)}{d t} \cdot (2 t - 2) - \frac{d (2 t - 2)}{d t} \cdot (3 t - 1)}{{(2 t - 2)}^{2}} [∵ \frac{d}{d x} (\frac{u}{v}) = \frac{\frac{d u}{d x} \cdot v - \frac{d v}{d x} \cdot u}{v^{2}}]

\Rightarrow \frac{d y}{d t} = \frac{(3 - 0) \cdot (2 t - 2) - (2 - 0) \cdot (3 t - 1)}{{(2 t - 2)}^{2}}

\Rightarrow \frac{d y}{d t} = \frac{6 t - 6 - 6 t + 2}{4 {(t - 1)}^{2}}

\Rightarrow \frac{d y}{d t} = \frac{- 4}{4 {(t - 1)}^{2}}

\Rightarrow \frac{d y}{d t} = - \frac{1}{{(t - 1)}^{2}}

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