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

The derivative of (6x-1(3x-5)^{-1}) is -(27)/((3x-5)^2)

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

The first derivative of (6x-1(3x-5)^{-1}) is -(27)/((3x-5)^2)

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

- \frac{27}{( 3 x - 5 ) ^{2}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

6 (3 x - 5)^{- 1} + (- \frac{3}{( 3 x - 5 ) ^{2}}) (6 x - 1) : - \frac{27}{( 3 x - 5 ) ^{2}}

= - \frac{27}{( 3 x - 5 ) ^{2}}

\frac{d}{d t} (a cos (3 t))

\frac{\partial}{\partial x} (e^{3 x^{2}} + 4 x y + 5 y^{2})

f (t) = t e^{t}

f (x) = cos (\frac{π x}{2}), at x = 0.7

x y d x - (x^{2} - x) d y = 0

What is the derivative of (6x-1(3x-5)^{-1}) ?
The derivative of (6x-1(3x-5)^{-1}) is -(27)/((3x-5)^2)
What is the first derivative of (6x-1(3x-5)^{-1}) ?
The first derivative of (6x-1(3x-5)^{-1}) is -(27)/((3x-5)^2)