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Popular >

derivative of x/(x-1)

Solution

derivative of

\frac{x}{x - 1}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial y)(sqrt(y-x)-z)

\frac{\partial}{\partial y} (y - x - z)

integral of (50+2x)^{3/2}

\int (50 + 2 x)^{\frac{3}{2}} d x

f(x)=5-3(1+x^2)^{-1}

f (x) = 5 - 3 (1 + x^{2})^{- 1}

limit as x approaches 1 of (2x^3-14x^2+12x)/(x^3-10x^2+27x-18)

x \to 1 lim (\frac{2 x ^{3} - 14 x ^{2} + 12 x}{x ^{3} - 10 x ^{2} + 27 x - 18})

x*(dy)/(dx)+y=y^2x^2ln(x)

x \cdot \frac{d y}{d x} + y = y^{2} x^{2} ln (x)

Frequently Asked Questions (FAQ)

What is the derivative of x/(x-1) ?
The derivative of x/(x-1) is -1/((x-1)^2)
What is the first derivative of x/(x-1) ?
The first derivative of x/(x-1) is -1/((x-1)^2)