What is (\partial)/(\partial y)((1-xy)^{-2}) ?

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

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(\partial)/(\partial y)((1-xy)^{-2})

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x ^{6}}{x ^{14} - 5} d x

f (x) = \frac{3 x + 5}{1 - x ^{2}}

f (x) = \frac{10 x}{x ^{2} - 6}

\int \frac{x ^{5}}{e ^{2 - 3 x^{6}}} d x

n = 1 \sum \infty \frac{1}{1 - 2 n}

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