What is the derivative of (4X-1)^2(3X-1)^{-2} ?

The derivative of (4X-1)^2(3X-1)^{-2} is (-8X+2)/((3X-1)^3)

What is the first derivative of (4X-1)^2(3X-1)^{-2} ?

The first derivative of (4X-1)^2(3X-1)^{-2} is (-8X+2)/((3X-1)^3)

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derivative of

(4 X - 1)^{2} (3 X - 1)^{- 2}

\frac{- 8 X + 2}{( 3 X - 1 ) ^{3}}

Solution steps

\frac{d}{d X} ((4 X - 1)^{2} (3 X - 1)^{- 2})

Apply the Product Rule:

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

f = (4 X - 1)^{2}, g = (3 X - 1)^{- 2}

= \frac{d}{d X} ((4 X - 1)^{2}) (3 X - 1)^{- 2} + \frac{d}{d X} ((3 X - 1)^{- 2}) (4 X - 1)^{2}

\frac{d}{d X} ((4 X - 1)^{2}) = 8 (4 X - 1)

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

= 8 (4 X - 1) (3 X - 1)^{- 2} + (- \frac{6}{( 3 X - 1 ) ^{3}}) (4 X - 1)^{2}

Simplify

8 (4 X - 1) (3 X - 1)^{- 2} + (- \frac{6}{( 3 X - 1 ) ^{3}}) (4 X - 1)^{2} : \frac{- 8 X + 2}{( 3 X - 1 ) ^{3}}

= \frac{- 8 X + 2}{( 3 X - 1 ) ^{3}}

\frac{d y}{d x} = 8 x y

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\int x^{2} - 7 d x

\int_{1}^{4} (1 - x) (x - 4) d x

What is the derivative of (4X-1)^2(3X-1)^{-2} ?
The derivative of (4X-1)^2(3X-1)^{-2} is (-8X+2)/((3X-1)^3)
What is the first derivative of (4X-1)^2(3X-1)^{-2} ?
The first derivative of (4X-1)^2(3X-1)^{-2} is (-8X+2)/((3X-1)^3)