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Popular >

derivative of (x+4/(x-5))

Solution

\frac{d}{d x} (\frac{x + 4}{x - 5})

Solution

- \frac{9}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 4}{x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 4 ) ( x - 5 ) - \frac{d}{d x} ( x - 5 ) ( x + 4 )}{( x - 5 ) ^{2}}

\frac{d}{d x} (x + 4) = 1

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

= \frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 4 )}{( x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 5 ) - 1 \cdot ( x + 4 )}{( x - 5 ) ^{2}} : - \frac{9}{( x - 5 ) ^{2}}

= - \frac{9}{( x - 5 ) ^{2}}

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\frac{d}{d x} (\frac{x ^{2} + 2 x}{4 x})

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\int_{1}^{2} \frac{1}{x ^{8}} d x

sum from n=1 to infinity of 2/((n+2)^3)

n = 1 \sum \infty \frac{2}{( n + 2 ) ^{3}}

derivative of e^{3x-3}

\frac{d}{d x} (e^{3 x - 3})

Frequently Asked Questions (FAQ)

What is the derivative of (x+4/(x-5)) ?
The derivative of (x+4/(x-5)) is -9/((x-5)^2)
What is the first derivative of (x+4/(x-5)) ?
The first derivative of (x+4/(x-5)) is -9/((x-5)^2)