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Popular >

derivative of (x-2/(x-1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral from 0 to 1 of 5x-5x^2

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

inverse oflaplace ((s+1)^2)/(s^2-s-6)inverse laplace

\frac{( s + 1 ) ^{2}}{s ^{2} - s - 6}

(\partial)/(\partial x)(sin(6x^3y-6xy^2))

\frac{\partial}{\partial x} (sin (6 x^{3} y - 6 x y^{2}))

derivative of 7/(x^8+5x+1)

\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

derivative of sin(14x)

\frac{d}{d x} (sin (14 x))

Frequently Asked Questions (FAQ)

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