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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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