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

The derivative of (x^2)/(x-1) is (x^2-2x)/((x-1)^2)

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

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

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derivative of

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

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

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

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

Simplify

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

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

\int \frac{1}{1 + 2 x ^{2} + x ^{4}} d x

\frac{4 + s}{s ^{2} + 3 s + 1}

\frac{\partial}{\partial x} (2 x^{3} y^{3} + 3 x + 4 y)

\frac{\partial}{\partial x} (4 x^{3} y^{3} + 4)

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