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Popular >

derivative of y= x/(x-1)

Solution

derivative of

y = \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

integral from 0 to 1 of 1-x^{2/5}

\int_{0}^{1} 1 - x^{\frac{2}{5}} d x

area f(x)=x^3-x^2-x,g(x)=x area

f (x) = x^{3} - x^{2} - x, g (x) = x

(2xy^3-3x^2y^2)dx+(xy^3+2x^2y^2)dy=0

(2 x y^{3} - 3 x^{2} y^{2}) d x + (x y^{3} + 2 x^{2} y^{2}) d y = 0

(dy)/(dt)=0.04y(400-y)

\frac{d y}{d t} = 0.04 y (400 - y)

integral of sqrt(\sqrt{x)-1}

\int x - 1 d x

Frequently Asked Questions (FAQ)

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