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

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

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

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

- 2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - 2 y

Simplify

= - 2 y

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

y = - x^{2} + 4, y = 3 x

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

\frac{d y}{d x} = 6 y e^{x + 9}

x \to 0 lim ((1 - \frac{1}{x})^{x})

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