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Popular >

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

Solution

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

Solution

\frac{8}{( x + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{8}{( x + 5 ) ^{2}}

Popular Examples

integral of sin^2(1/3 x)

\int sin^{2} (\frac{1}{3} x) d x

inverse oflaplace s/((s^2+5^2)^2)inverse laplace

\frac{s}{( s ^{2} + 5 ^{2} ) ^{2}}

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\int \frac{4 + x ^{2}}{x} d x

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

limit as x approaches 0 of (4e^x-4)/x

x \to 0 lim (\frac{4 e ^{x} - 4}{x})

Frequently Asked Questions (FAQ)

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