What is the derivative of f(x)=(4x-1)^{-2} ?

The derivative of f(x)=(4x-1)^{-2} is -8/((4x-1)^3)

What is the first derivative of f(x)=(4x-1)^{-2} ?

The first derivative of f(x)=(4x-1)^{-2} is -8/((4x-1)^3)

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derivative of

f (x) = (4 x - 1)^{- 2}

- \frac{8}{( 4 x - 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{2}{( 4 x - 1 ) ^{3}} \cdot 4 : - \frac{8}{( 4 x - 1 ) ^{3}}

= - \frac{8}{( 4 x - 1 ) ^{3}}

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