What is (\partial)/(\partial x)(-(7x^2)/((x-y)^2)) ?

The answer to (\partial)/(\partial x)(-(7x^2)/((x-y)^2)) is (14xy)/((x-y)^3)

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(\partial)/(\partial x)(-(7x^2)/((x-y)^2))

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

\frac{14 x y}{( x - y ) ^{3}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

= - 7 \cdot \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)

= - 7 \cdot \frac{2 x ( x - y ) ^{2} - 2 ( x - y ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}}

Simplify

- 7 \cdot \frac{2 x ( x - y ) ^{2} - 2 ( x - y ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}} : \frac{14 x y}{( x - y ) ^{3}}

= \frac{14 x y}{( x - y ) ^{3}}

\frac{d}{d x} (a x^{b^{2} - c})

\frac{\partial}{\partial x} (x y + 2 z)

f (x) = x^{- \frac{1}{5}} + x^{\frac{1}{5}}

x \to 1 - lim (G (x))

x \to - \infty lim (- 5^{x})

What is (\partial)/(\partial x)(-(7x^2)/((x-y)^2)) ?
The answer to (\partial)/(\partial x)(-(7x^2)/((x-y)^2)) is (14xy)/((x-y)^3)