What is (\partial)/(\partial x)(x/(x-1)) ?

The answer to (\partial)/(\partial x)(x/(x-1)) is -1/((x-1)^2)

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(\partial)/(\partial x)(x/(x-1))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial 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}}

x \to 0 lim (2 x^{2} cos (\frac{5}{x}))

f (x) = 5 x^{5} ln (x)

\frac{d y}{d x} = \frac{y}{x} + 5 x + 4

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

\frac{\partial}{\partial x} (14 x e^{y})

What is (\partial)/(\partial x)(x/(x-1)) ?
The answer to (\partial)/(\partial x)(x/(x-1)) is -1/((x-1)^2)