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

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

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

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

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

Solution steps

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

Simplify

\frac{x}{y} + \frac{1}{x} + \frac{1}{y} : \frac{x + 1}{y} + \frac{1}{x}

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\int_{- 1}^{3} x^{3} d x

x \to 2 lim (6^{x} + 2)

\int (3 x - 2)^{3} d x

x \to 0 lim (2 x - 3)

(- 2.7) (20.16)

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