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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x - y ^{2}} (- 2 y) : - \frac{y}{x - y ^{2}}

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

x \to 0 lim (\frac{6 x ^{2}}{x ^{2}})

\frac{\partial}{\partial x} (e^{- x^{5} - y^{3}})

y + 2 y^{^{'}} + 5 y = 4 \cdot e^{- t} \cdot cos (2 t)

\frac{x - 2}{x - 2}

u \to 2 + lim (u^{2})

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