What is the derivative of (5x-1(6x-3)^{-1}) ?

The derivative of (5x-1(6x-3)^{-1}) is -1/((2x-1)^2)

What is the first derivative of (5x-1(6x-3)^{-1}) ?

The first derivative of (5x-1(6x-3)^{-1}) is -1/((2x-1)^2)

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\frac{d}{d x} ((5 x - 1) (6 x - 3)^{- 1})

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

Solution steps

\frac{d}{d x} ((5 x - 1) (6 x - 3)^{- 1})

Apply the Product Rule:

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

f = 5 x - 1, g = (6 x - 3)^{- 1}

= \frac{d}{d x} (5 x - 1) (6 x - 3)^{- 1} + \frac{d}{d x} ((6 x - 3)^{- 1}) (5 x - 1)

\frac{d}{d x} (5 x - 1) = 5

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

= 5 (6 x - 3)^{- 1} + (- \frac{2}{3 ( 2 x - 1 ) ^{2}}) (5 x - 1)

Simplify

5 (6 x - 3)^{- 1} + (- \frac{2}{3 ( 2 x - 1 ) ^{2}}) (5 x - 1) : - \frac{1}{( 2 x - 1 ) ^{2}}

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

\frac{d}{d x} (1 + 3^{x})

x \to 2 π lim (x)

sec^{2} (θ) - 3

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} + 1})

What is the derivative of (5x-1(6x-3)^{-1}) ?
The derivative of (5x-1(6x-3)^{-1}) is -1/((2x-1)^2)
What is the first derivative of (5x-1(6x-3)^{-1}) ?
The first derivative of (5x-1(6x-3)^{-1}) is -1/((2x-1)^2)