What is the derivative of (3t-1)(2t-2)^{-1} ?

The derivative of (3t-1)(2t-2)^{-1} is -1/((t-1)^2)

What is the first derivative of (3t-1)(2t-2)^{-1} ?

The first derivative of (3t-1)(2t-2)^{-1} is -1/((t-1)^2)

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derivative of

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

- \frac{1}{( t - 1 ) ^{2}}

Solution steps

\frac{d}{d t} ((3 t - 1) (2 t - 2)^{- 1})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 t - 1, g = (2 t - 2)^{- 1}

= \frac{d}{d t} (3 t - 1) (2 t - 2)^{- 1} + \frac{d}{d t} ((2 t - 2)^{- 1}) (3 t - 1)

\frac{d}{d t} (3 t - 1) = 3

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

= 3 (2 t - 2)^{- 1} + (- \frac{1}{2 ( t - 1 ) ^{2}}) (3 t - 1)

Simplify

3 (2 t - 2)^{- 1} + (- \frac{1}{2 ( t - 1 ) ^{2}}) (3 t - 1) : - \frac{1}{( t - 1 ) ^{2}}

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

What is the derivative of (3t-1)(2t-2)^{-1} ?
The derivative of (3t-1)(2t-2)^{-1} is -1/((t-1)^2)
What is the first derivative of (3t-1)(2t-2)^{-1} ?
The first derivative of (3t-1)(2t-2)^{-1} is -1/((t-1)^2)