What is (\partial)/(\partial y)(sqrt(x^2+y^2-1)) ?

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

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(\partial)/(\partial y)(sqrt(x^2+y^2-1))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} ((x^{2} - 5 x + 1) (2 x + 3))

\frac{\partial}{\partial y} (\frac{( a x + b y )}{c x + d y})

y^{^{''}} = e^{(3 t)}

- x^{2} + 5 x, x^{2} - 3 x

\int_{4}^{5} \frac{x}{x ^{2} + 6 x + 13} d x

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