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Popular >

derivative of (x-5/(x+3))

Solution

\frac{d}{d x} (\frac{x - 5}{x + 3})

Solution

\frac{8}{( x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( x - 5 )}{( x + 3 ) ^{2}}

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

\frac{d}{d x} (x + 3) = 1

= \frac{1 \cdot ( x + 3 ) - 1 \cdot ( x - 5 )}{( x + 3 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 3 ) - 1 \cdot ( x - 5 )}{( x + 3 ) ^{2}} : \frac{8}{( x + 3 ) ^{2}}

= \frac{8}{( x + 3 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x-5/(x+3)) ?
The derivative of (x-5/(x+3)) is 8/((x+3)^2)
What is the first derivative of (x-5/(x+3)) ?
The first derivative of (x-5/(x+3)) is 8/((x+3)^2)