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

The derivative of (6x-1(5x-2)^{-1}) is -7/((5x-2)^2)

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

The first derivative of (6x-1(5x-2)^{-1}) is -7/((5x-2)^2)

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\frac{d}{d x} ((6 x - 1) (5 x - 2)^{- 1})

- \frac{7}{( 5 x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} ((6 x - 1) (5 x - 2)^{- 1})

Apply the Product Rule:

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

f = 6 x - 1, g = (5 x - 2)^{- 1}

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

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

\frac{d}{d x} ((5 x - 2)^{- 1}) = - \frac{5}{( 5 x - 2 ) ^{2}}

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

Simplify

6 (5 x - 2)^{- 1} + (- \frac{5}{( 5 x - 2 ) ^{2}}) (6 x - 1) : - \frac{7}{( 5 x - 2 ) ^{2}}

= - \frac{7}{( 5 x - 2 ) ^{2}}

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

y^{^{''}} + 4 y^{^{'}} + 5 y = - 10 x + 3 e^{- x}

x \to 3 lim (x - 2)

\int \frac{sec ^{2} ( x )}{x} d x

f (x) = \frac{x + 5}{x - 5}

What is the derivative of (6x-1(5x-2)^{-1}) ?
The derivative of (6x-1(5x-2)^{-1}) is -7/((5x-2)^2)
What is the first derivative of (6x-1(5x-2)^{-1}) ?
The first derivative of (6x-1(5x-2)^{-1}) is -7/((5x-2)^2)