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Popular >

derivative of x/(x-2)

Solution

derivative of

\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

derivative of (2x/3+(x+1)^{2/3})

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

1/5 (dy)/(dx)=(1/5)^2-1/5

\frac{1}{5} \frac{d y}{d x} = (\frac{1}{5})^{2} - \frac{1}{5}

derivative of y+xcos(y)

\frac{d}{d x} (y + x cos (y))

inverse oflaplace (5x+5)/(x^2-4)inverse laplace

\frac{5 x + 5}{x ^{2} - 4}

integral of (e^{ln(x)})/(x^2)

\int \frac{e ^{l n (x)}}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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