What is the derivative of (4t-1)(3t-6)^{-1} ?

The derivative of (4t-1)(3t-6)^{-1} is -7/(3(t-2)^2)

What is the first derivative of (4t-1)(3t-6)^{-1} ?

The first derivative of (4t-1)(3t-6)^{-1} is -7/(3(t-2)^2)

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derivative of

(4 t - 1) (3 t - 6)^{- 1}

- \frac{7}{3 ( t - 2 ) ^{2}}

Solution steps

\frac{d}{d t} ((4 t - 1) (3 t - 6)^{- 1})

Apply the Product Rule:

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

f = 4 t - 1, g = (3 t - 6)^{- 1}

= \frac{d}{d t} (4 t - 1) (3 t - 6)^{- 1} + \frac{d}{d t} ((3 t - 6)^{- 1}) (4 t - 1)

\frac{d}{d t} (4 t - 1) = 4

\frac{d}{d t} ((3 t - 6)^{- 1}) = - \frac{1}{3 ( t - 2 ) ^{2}}

= 4 (3 t - 6)^{- 1} + (- \frac{1}{3 ( t - 2 ) ^{2}}) (4 t - 1)

Simplify

4 (3 t - 6)^{- 1} + (- \frac{1}{3 ( t - 2 ) ^{2}}) (4 t - 1) : - \frac{7}{3 ( t - 2 ) ^{2}}

= - \frac{7}{3 ( t - 2 ) ^{2}}

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 1

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What is the derivative of (4t-1)(3t-6)^{-1} ?
The derivative of (4t-1)(3t-6)^{-1} is -7/(3(t-2)^2)
What is the first derivative of (4t-1)(3t-6)^{-1} ?
The first derivative of (4t-1)(3t-6)^{-1} is -7/(3(t-2)^2)