What is (\partial)/(\partial x)(1/x+1/y) ?

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

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(\partial)/(\partial x)(1/x+1/y)

\frac{\partial}{\partial x} (\frac{1}{x} + \frac{1}{y})

- \frac{1}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x} + \frac{1}{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= - \frac{1}{x ^{2}} + 0

Simplify

= - \frac{1}{x ^{2}}

\frac{d}{d x} ((4 - x^{\frac{2}{3}})^{\frac{3}{2}})

e^{- 3 x^{2}}

\int \frac{1}{4 t} d t

x \to 6 lim (f (x) - g (x))

\frac{d ^{2}}{d x ^{2}} (6 cos (3 x + 3))

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