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Popular >

derivative of x/(x-7)

Solution

derivative of

\frac{x}{x - 7}

Solution

- \frac{7}{( x - 7 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

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\int (sin^{2} (x) cos (x)) d x

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f (x) = - x^{2} + 2, g (x) = - x - 4

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\int \frac{- 2}{x + 1} d x

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Frequently Asked Questions (FAQ)

What is the derivative of x/(x-7) ?
The derivative of x/(x-7) is -7/((x-7)^2)
What is the first derivative of x/(x-7) ?
The first derivative of x/(x-7) is -7/((x-7)^2)