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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

\int 7 x e^{x} d x

y = x, y = x

4 cos (x^{2})

x \to 3 lim (\frac{1}{x ^{2} - 9})

t \to π lim (tan (\frac{t}{6}))

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