What is the derivative of (x+10/(x-10)) ?

The derivative of (x+10/(x-10)) is -(20)/((x-10)^2)

What is the first derivative of (x+10/(x-10)) ?

The first derivative of (x+10/(x-10)) is -(20)/((x-10)^2)

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\frac{d}{d x} (\frac{x + 10}{x - 10})

- \frac{20}{( x - 10 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 10}{x - 10})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 10 ) ( x - 10 ) - \frac{d}{d x} ( x - 10 ) ( x + 10 )}{( x - 10 ) ^{2}}

\frac{d}{d x} (x + 10) = 1

\frac{d}{d x} (x - 10) = 1

= \frac{1 \cdot ( x - 10 ) - 1 \cdot ( x + 10 )}{( x - 10 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 10 ) - 1 \cdot ( x + 10 )}{( x - 10 ) ^{2}} : - \frac{20}{( x - 10 ) ^{2}}

= - \frac{20}{( x - 10 ) ^{2}}

What is the derivative of (x+10/(x-10)) ?
The derivative of (x+10/(x-10)) is -(20)/((x-10)^2)
What is the first derivative of (x+10/(x-10)) ?
The first derivative of (x+10/(x-10)) is -(20)/((x-10)^2)