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

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

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

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

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derivative of

(4 x + 5)^{- 1}

- \frac{4}{( 4 x + 5 ) ^{2}}

Solution steps

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

Apply the chain rule:

- \frac{1}{( 4 x + 5 ) ^{2}} \frac{d}{d x} (4 x + 5)

= - \frac{1}{( 4 x + 5 ) ^{2}} \frac{d}{d x} (4 x + 5)

\frac{d}{d x} (4 x + 5) = 4

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

Simplify

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

= - \frac{4}{( 4 x + 5 ) ^{2}}

n = 0 \sum \infty \frac{3}{4 ^{n}}

\frac{d}{d x} (x^{2} π)

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

\frac{3 x}{8 - cot ( x )}

f (x) = 5^{- \frac{x}{2}} sin (2 x)

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