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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d}{d x} (ln ((x + 6)^{11}))

\int \frac{x ^{3} + x}{x} d x

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

\int_{0}^{0.1} x arctan (3 x) d x

\frac{d}{d x} (1. 5^{1.7 x})

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