What is (\partial)/(\partial l)(2pisqrt(l/({g))}) ?

The answer to (\partial)/(\partial l)(2pisqrt(l/({g))}) is pi/(sqrt(l)\sqrt{{g)}}

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(\partial)/(\partial l)(2pisqrt(l/({g))})

\frac{\partial}{\partial l} (2 π \frac{l}{g})

\frac{π}{l g}

Solution steps

\frac{\partial}{\partial l} (2 π \frac{l}{g})

Take the constant out:

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

= 2 π \frac{\partial}{\partial l} (\frac{l}{g})

Apply the chain rule:

\frac{1}{2 \frac{l}{g}} \frac{\partial}{\partial l} (\frac{l}{g})

= \frac{1}{2 \frac{l}{g}} \frac{\partial}{\partial l} (\frac{l}{g})

\frac{\partial}{\partial l} (\frac{l}{g}) = \frac{1}{g}

= 2 π \frac{1}{2 \frac{l}{g}} \cdot \frac{1}{g}

Simplify

2 π \frac{1}{2 \frac{l}{g}} \cdot \frac{1}{g} : \frac{π}{l g}

= \frac{π}{l g}

What is (\partial)/(\partial l)(2pisqrt(l/({g))}) ?
The answer to (\partial)/(\partial l)(2pisqrt(l/({g))}) is pi/(sqrt(l)\sqrt{{g)}}