What is (\partial)/(\partial u)(sqrt(uv)) ?

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

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(\partial)/(\partial u)(sqrt(uv))

\frac{\partial}{\partial u} (uv)

\frac{v}{2 u}

Solution steps

\frac{\partial}{\partial u} (uv)

Treat

v

as a constant

Apply the chain rule:

\frac{1}{2 uv} \frac{\partial}{\partial u} (uv)

= \frac{1}{2 uv} \frac{\partial}{\partial u} (uv)

\frac{\partial}{\partial u} (uv) = v

= \frac{1}{2 uv} v

Simplify

\frac{1}{2 uv} v : \frac{v}{2 u}

= \frac{v}{2 u}

\frac{d y}{d x} = \frac{- 0.1}{cos ( y )}

y = x^{(3)}, y = x^{(6)}

g (x) = 5 e^{x} x

n = 0 \sum \infty (x - 1)^{n}

x \to 0 lim (\frac{x - 3}{x - 3})

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