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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (ln (6 y e^{x y}))

\int (8 + π) d x

\frac{d}{d x} ((1 + arccos (3 x))^{3})

\int ∣ 2 x ∣ d x

f (x) = 3 x^{5} e^{2 x}

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