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Popular >

derivative of f(x)= x/(x-2)

Solution

derivative of

f (x) = \frac{x}{x - 2}

Solution

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

Solution steps

\frac{d}{d x} (\frac{x}{x - 2})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 2) = 1

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

Simplify

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

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

Popular Examples

integral of 1/(3t-1)

\int \frac{1}{3 t - 1} d t

limit as n approaches infinity of (3n^2+7n+11)/(8n^2-5n+3)

n \to \infty lim (\frac{3 n ^{2} + 7 n + 11}{8 n ^{2} - 5 n + 3})

integral of 4x+6

\int 4 x + 6 d x

integral of 5/(xsqrt(1-25ln^2(x)))

\int \frac{5}{x 1 - 25 ln ^{2} ( x )} d x

integral of 1/(2x+x^2)

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

Frequently Asked Questions (FAQ)

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