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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

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

= 0 - (- \frac{2}{x ^{3}})

Simplify

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

\frac{\partial}{\partial y} (5 x^{2} y^{2})

x d y - (2 x e^{\frac{- y}{x}} + y) d x = 0

\frac{d}{d θ} (8 cos (θ) + 2 sin (θ))

\frac{d y}{d x} - x e^{y} = 2 e^{y}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = e^{- x} \cdot ln (x)

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