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

The answer to (\partial)/(\partial {g)}(2pisqrt(l/({g))}) is -(pisqrt(l))/({g)^{3/2}}

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

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

- \frac{π l}{g ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial g} (\frac{l}{g}) = - \frac{l}{g ^{2}}

= 2 π \frac{1}{2 \frac{l}{g}} (- \frac{l}{g ^{2}})

Simplify

2 π \frac{1}{2 \frac{l}{g}} (- \frac{l}{g ^{2}}) : - \frac{π l}{g ^{\frac{3}{2}}}

= - \frac{π l}{g ^{\frac{3}{2}}}

(t - 1)^{2}

\int e^{4 l n (x)} d x

\frac{d}{d x} (\frac{x ^{3}}{2})

x \to 2 + lim (4 x^{2} - 2 x + 3)

f (x) = 7 x, at x = 25

What is (\partial)/(\partial {g)}(2pisqrt(l/({g))}) ?
The answer to (\partial)/(\partial {g)}(2pisqrt(l/({g))}) is -(pisqrt(l))/({g)^{3/2}}