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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

x (cos (x^{2}))

\frac{( x ^{2} - 4 )}{( x ^{2} - 1 )}

\int \frac{9 x ^{2} - 8 x + 8}{x ( x ^{2} + 4 )} d x

n = 0 \sum \infty \frac{n}{n + 2}

\frac{d}{d x} (\frac{x}{1 - 2 x})

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