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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x + 2) = 4

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

Simplify

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

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

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