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Popular Calculus >

derivative of y=((x+7))/((x-5))

Solution

derivative of

y = \frac{( x + 7 )}{( x - 5 )}

Solution

- \frac{12}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 7}{x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 7 ) ( x - 5 ) - \frac{d}{d x} ( x - 5 ) ( x + 7 )}{( x - 5 ) ^{2}}

\frac{d}{d x} (x + 7) = 1

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

= \frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 7 )}{( x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 7 )}{( x - 5 ) ^{2}} : - \frac{12}{( x - 5 ) ^{2}}

= - \frac{12}{( x - 5 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=((x+7))/((x-5)) ?
The derivative of y=((x+7))/((x-5)) is -(12)/((x-5)^2)
What is the first derivative of y=((x+7))/((x-5)) ?
The first derivative of y=((x+7))/((x-5)) is -(12)/((x-5)^2)