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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{4 x ^{4} + x + 1}{x ^{5} + x ^{4}} d x

ln (225 sin^{2} (x))

y = \frac{1}{x}

\int_{1}^{\infty} x^{- 3} d x

y^{^{'}} - 5 y = 4 e^{7 t}

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