What is (\partial)/(\partial t)(sqrt(1+t)) ?

The answer to (\partial)/(\partial t)(sqrt(1+t)) is 1/(2sqrt(1+t))

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(\partial)/(\partial t)(sqrt(1+t))

\frac{\partial}{\partial t} (1 + t)

\frac{1}{2 1 + t}

Solution steps

\frac{\partial}{\partial t} (1 + t)

Apply the chain rule:

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

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

\frac{\partial}{\partial t} (1 + t) = 1

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

Simplify

= \frac{1}{2 1 + t}

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What is (\partial)/(\partial t)(sqrt(1+t)) ?
The answer to (\partial)/(\partial t)(sqrt(1+t)) is 1/(2sqrt(1+t))