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Popular >

derivative of ((x+8)/(x^2))

Solution

\frac{d}{d x} (\frac{( x + 8 )}{x ^{2}})

Solution

\frac{- x - 16}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{( x + 8 )}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 8 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x + 8 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x + 8) = 1

\frac{d}{d x} (x^{2}) = 2 x

= \frac{1 \cdot x ^{2} - 2 x ( x + 8 )}{( x ^{2} ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} - 2 x ( x + 8 )}{( x ^{2} ) ^{2}} : \frac{- x - 16}{x ^{3}}

= \frac{- x - 16}{x ^{3}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ((x+8)/(x^2)) ?
The derivative of ((x+8)/(x^2)) is (-x-16)/(x^3)
What is the first derivative of ((x+8)/(x^2)) ?
The first derivative of ((x+8)/(x^2)) is (-x-16)/(x^3)