What is the derivative of (2t-1)(4t-6)^{-1} ?

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

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

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

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derivative of

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

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

Solution steps

\frac{d}{d t} ((2 t - 1) (4 t - 6)^{- 1})

Apply the Product Rule:

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

f = 2 t - 1, g = (4 t - 6)^{- 1}

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

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

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

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

Simplify

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

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

x^{2} y^{^{''}} - 2 y = 0, y (1) = 0, y^{^{'}} (1) = 3

x \to + 0 lim (x^{8} - \frac{1}{x})

x \to 1 - lim (\frac{x - 1}{∣ x - 1 ∣})

\int - x sin (y) + 2 y d y

\int x (x + 9)^{10} d x

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