What is (\partial)/(\partial x)((x^2y-1)/(x^2)) ?

The answer to (\partial)/(\partial x)((x^2y-1)/(x^2)) is 2/(x^3)

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(\partial)/(\partial x)((x^2y-1)/(x^2))

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

\frac{2}{x ^{3}}

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 y x x ^{2} - 2 x ( x ^{2} y - 1 )}{( x ^{2} ) ^{2}} : \frac{2}{x ^{3}}

= \frac{2}{x ^{3}}

\frac{d}{d x} (21 x)

\frac{\partial}{\partial x} (20 - x^{2} - 7 y^{2})

\frac{d}{d x} (ln (\frac{1 + e ^{x}}{1 - e ^{x}}))

\int (x - 1)^{3} d x

\int \frac{1}{( x + 1 ) ^{3}} d x

What is (\partial)/(\partial x)((x^2y-1)/(x^2)) ?
The answer to (\partial)/(\partial x)((x^2y-1)/(x^2)) is 2/(x^3)