What is (\partial)/(\partial x)(sqrt(9+x^2+y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(9+x^2+y^2)) is x/(sqrt(9+x^2+y^2))

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(\partial)/(\partial x)(sqrt(9+x^2+y^2))

\frac{\partial}{\partial x} (9 + x^{2} + y^{2})

\frac{x}{9 + x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (9 + x^{2} + y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 9 + x ^{2} + y ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

= \frac{1}{2 9 + x ^{2} + y ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

\frac{\partial}{\partial x} (9 + x^{2} + y^{2}) = 2 x

= \frac{1}{2 9 + x ^{2} + y ^{2}} \cdot 2 x

Simplify

\frac{1}{2 9 + x ^{2} + y ^{2}} \cdot 2 x : \frac{x}{9 + x ^{2} + y ^{2}}

= \frac{x}{9 + x ^{2} + y ^{2}}

\frac{d ^{2}}{d x ^{2}} (\frac{10}{3 x ^{3}})

\frac{\partial}{\partial x} (x^{2} - x y^{2} + 4 y^{5})

f (x) = 12 x

\frac{d}{d x} ((\frac{x ^{2} + 1}{2 x + 1})^{2})

\frac{d y}{d x} = 15 - \frac{3 y}{290}

What is (\partial)/(\partial x)(sqrt(9+x^2+y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(9+x^2+y^2)) is x/(sqrt(9+x^2+y^2))