What is (\partial)/(\partial u)(1/3 (u+v)) ?

The answer to (\partial)/(\partial u)(1/3 (u+v)) is 1/3

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(\partial)/(\partial u)(1/3 (u+v))

\frac{\partial}{\partial u} (\frac{1}{3} (u + v))

\frac{1}{3}

Solution steps

\frac{\partial}{\partial u} (\frac{1}{3} (u + v))

Treat

v

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{\partial}{\partial u} (u + v)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{3} (\frac{\partial}{\partial u} (u) + \frac{\partial}{\partial u} (v))

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

\frac{\partial}{\partial u} (v) = 0

= \frac{1}{3} (1 + 0)

Simplify

= \frac{1}{3}

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What is (\partial)/(\partial u)(1/3 (u+v)) ?
The answer to (\partial)/(\partial u)(1/3 (u+v)) is 1/3