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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (arcsin (x - y))

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

y = x^{2}, at x = \frac{1}{3}

\frac{\partial}{\partial y} (\frac{5 ( y + 2 )}{( x + 2 ) ^{2}})

\frac{\partial}{\partial x} (y^{x} - ln (x^{4} y + 6 x))

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