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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

2 x^{2} - 3

e^{- s}

y^{^{''}} - 2 y^{^{'}} - 3 y = - 5 t e^{- t}

f (x) = 12

x \to - 3 lim (x + 7)

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