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{1}{b - m t}

n = 5 \sum \infty cos (\frac{1}{n ^{3}})

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

\frac{99 x ^{\frac{7}{2}}}{4}

\int \frac{2 x + 6}{( ( x + 1 ) ^{2} + 9 ) ^{4}} d 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))