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

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

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

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

2 x - y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

= 2 x + 0 - y^{2} - 0

Simplify

= 2 x - y^{2}

x \to \infty + lim (x^{3})

x \to 0 - lim (18 - \frac{4}{x ^{3}})

\frac{d}{d x} (e^{x s i n h (x)})

x \to \infty lim (2 x + 3)

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