What is the derivative of 5(4x-3)^{-1} ?

The derivative of 5(4x-3)^{-1} is -(20)/((4x-3)^2)

What is the first derivative of 5(4x-3)^{-1} ?

The first derivative of 5(4x-3)^{-1} is -(20)/((4x-3)^2)

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derivative

- \frac{20}{( 4 x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (5 (4 x - 3)^{- 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} ((4 x - 3)^{- 1})

Apply the chain rule:

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

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

\frac{d}{d x} (4 x - 3) = 4

= 5 (- \frac{1}{( 4 x - 3 ) ^{2}} \cdot 4)

Simplify

5 (- \frac{1}{( 4 x - 3 ) ^{2}} \cdot 4) : - \frac{20}{( 4 x - 3 ) ^{2}}

= - \frac{20}{( 4 x - 3 ) ^{2}}

What is the derivative of 5(4x-3)^{-1} ?
The derivative of 5(4x-3)^{-1} is -(20)/((4x-3)^2)
What is the first derivative of 5(4x-3)^{-1} ?
The first derivative of 5(4x-3)^{-1} is -(20)/((4x-3)^2)