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Popular >

derivative of x/(sqrt(x-1))

Solution

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

Solution

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

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

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

Simplify

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

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

Popular Examples

integral of (4x^2)/(x^2)

\int \frac{4 x ^{2}}{x ^{2}} d x

integral of (2x^2+9x+2)/((x^2+1)^2)

\int \frac{2 x ^{2} + 9 x + 2}{( x ^{2} + 1 ) ^{2}} d x

derivative of (y^2-x^2/((x^2+y^2)^2))

\frac{d}{d x} (\frac{y ^{2} - x ^{2}}{( x ^{2} + y ^{2} ) ^{2}})

integral from 0 to 1 of tan(pi/4 x)

\int_{0}^{1} tan (\frac{π}{4} x) d x

integral of sin^2(x)-cos^2(x)

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

Frequently Asked Questions (FAQ)

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