What is the derivative of 1/(x+6) ?

The derivative of 1/(x+6) is -1/((x+6)^2)

What is the first derivative of 1/(x+6) ?

The first derivative of 1/(x+6) is -1/((x+6)^2)

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derivative of

\frac{1}{x + 6}

- \frac{1}{( x + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x + 6})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x + 6)^{- 1})

Apply the chain rule:

- \frac{1}{( x + 6 ) ^{2}} \frac{d}{d x} (x + 6)

= - \frac{1}{( x + 6 ) ^{2}} \frac{d}{d x} (x + 6)

\frac{d}{d x} (x + 6) = 1

= - \frac{1}{( x + 6 ) ^{2}} \cdot 1

Simplify

= - \frac{1}{( x + 6 ) ^{2}}

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x \to 0 - lim (\frac{x + 10}{x ^{2}})

\int (8 x^{4} + 4 x^{3} - 6 x^{2} - 4 x + 5) d x

What is the derivative of 1/(x+6) ?
The derivative of 1/(x+6) is -1/((x+6)^2)
What is the first derivative of 1/(x+6) ?
The first derivative of 1/(x+6) is -1/((x+6)^2)