What is (\partial)/(\partial x)(sqrt(x^2+y^2-5)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+y^2-5)) is x/(sqrt(x^2+y^2-5))

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(\partial)/(\partial x)(sqrt(x^2+y^2-5))

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

\frac{x}{x ^{2} + y ^{2} - 5}

Solution steps

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{2} + y ^{2} - 5} \frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

= \frac{1}{2 x ^{2} + y ^{2} - 5} \frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5) = 2 x

= \frac{1}{2 x ^{2} + y ^{2} - 5} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + y ^{2} - 5} \cdot 2 x : \frac{x}{x ^{2} + y ^{2} - 5}

= \frac{x}{x ^{2} + y ^{2} - 5}

What is (\partial)/(\partial x)(sqrt(x^2+y^2-5)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+y^2-5)) is x/(sqrt(x^2+y^2-5))