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Popular >

derivative of (x+9/(x-9))

Solution

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

Solution

- \frac{18}{( x - 9 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{1 \cdot ( x - 9 ) - 1 \cdot ( x + 9 )}{( x - 9 ) ^{2}} : - \frac{18}{( x - 9 ) ^{2}}

= - \frac{18}{( x - 9 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (x+9/(x-9)) ?
The derivative of (x+9/(x-9)) is -(18)/((x-9)^2)
What is the first derivative of (x+9/(x-9)) ?
The first derivative of (x+9/(x-9)) is -(18)/((x-9)^2)