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))

(\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}

d er i v a t i v e \frac{1}{b - m t}

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

p a r t ia l f r a c t i o n \frac{x ^{2}}{x ^{2} - 1}

d er i v a t i v e f (x) = \frac{375}{x ^{4}}

\frac{d}{d x} (10 x + 5)

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))