What is the derivative of 1/(x-9) ?

The derivative of 1/(x-9) is -1/((x-9)^2)

What is the first derivative of 1/(x-9) ?

The first derivative of 1/(x-9) is -1/((x-9)^2)

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derivative of

\frac{1}{x - 9}

- \frac{1}{( x - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x - 9})

Apply exponent rule:

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

= \frac{d}{d x} ((x - 9)^{- 1})

Apply the chain rule:

- \frac{1}{( x - 9 ) ^{2}} \frac{d}{d x} (x - 9)

= - \frac{1}{( x - 9 ) ^{2}} \frac{d}{d x} (x - 9)

\frac{d}{d x} (x - 9) = 1

= - \frac{1}{( x - 9 ) ^{2}} \cdot 1

Simplify

= - \frac{1}{( x - 9 ) ^{2}}

\frac{d}{d x} (\frac{1 - 6 x}{5 + x})

\int \frac{1}{8 - x} d x

\frac{d}{d x} (7 x + 8)

z e^{z}

What is the derivative of 1/(x-9) ?
The derivative of 1/(x-9) is -1/((x-9)^2)
What is the first derivative of 1/(x-9) ?
The first derivative of 1/(x-9) is -1/((x-9)^2)