What is (\partial)/(\partial u)(sqrt(u^2+v^2)) ?

The answer to (\partial)/(\partial u)(sqrt(u^2+v^2)) is u/(sqrt(u^2+v^2))

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(\partial)/(\partial u)(sqrt(u^2+v^2))

\frac{\partial}{\partial u} (u^{2} + v^{2})

\frac{u}{u ^{2} + v ^{2}}

Solution steps

\frac{\partial}{\partial u} (u^{2} + v^{2})

Treat

v

as a constant

Apply the chain rule:

\frac{1}{2 u ^{2} + v ^{2}} \frac{\partial}{\partial u} (u^{2} + v^{2})

= \frac{1}{2 u ^{2} + v ^{2}} \frac{\partial}{\partial u} (u^{2} + v^{2})

\frac{\partial}{\partial u} (u^{2} + v^{2}) = 2 u

= \frac{1}{2 u ^{2} + v ^{2}} \cdot 2 u

Simplify

\frac{1}{2 u ^{2} + v ^{2}} \cdot 2 u : \frac{u}{u ^{2} + v ^{2}}

= \frac{u}{u ^{2} + v ^{2}}

\int \frac{6 ln ( 4 x )}{5} d x

- 2 sin (x)

f (x) = x^{5} - 3 x + 4

\frac{e ^{x}}{x + 1}

x \to 1 lim (∣ x - 1 ∣)

What is (\partial)/(\partial u)(sqrt(u^2+v^2)) ?
The answer to (\partial)/(\partial u)(sqrt(u^2+v^2)) is u/(sqrt(u^2+v^2))