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

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

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

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

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

Solution steps

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

Treat

v, w

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

\frac{d}{d x} ((sin (\frac{x}{4}) + cos (x))^{\frac{1}{x}})

(1 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

x \to 8 + lim (\frac{3}{x - 8})

\int ln ((7 x)^{2}) d x

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