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

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

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

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

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derivative of

(x + 5)^{- 1}

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + 5) = 1

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

Simplify

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

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\frac{d}{d x} (lo g_{10} (1 + x^{2} y^{2}))

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