What is (\partial)/(\partial t)(sqrt(5t)) ?

The answer to (\partial)/(\partial t)(sqrt(5t)) is (sqrt(5))/(2sqrt(t))

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(\partial)/(\partial t)(sqrt(5t))

\frac{\partial}{\partial t} (5 t)

\frac{5}{2 t}

Solution steps

\frac{\partial}{\partial t} (5 t)

Apply the chain rule:

\frac{1}{2 5 t} \frac{\partial}{\partial t} (5 t)

= \frac{1}{2 5 t} \frac{\partial}{\partial t} (5 t)

\frac{\partial}{\partial t} (5 t) = 5

= \frac{1}{2 5 t} \cdot 5

Simplify

\frac{1}{2 5 t} \cdot 5 : \frac{5}{2 t}

= \frac{5}{2 t}

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What is (\partial)/(\partial t)(sqrt(5t)) ?
The answer to (\partial)/(\partial t)(sqrt(5t)) is (sqrt(5))/(2sqrt(t))