Solve t = 2pi sqrt l/g

Evaluate

t = 2 π \times \frac{l}{g}

Multiply the terms

t = \frac{2 π l}{g}

Find the first partial derivative by treating the variable g as a constant and differentiating with respect to l

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

Use differentiation rule \frac{\partial}{\partial x} (\frac{f ( x )}{g ( x )}) = \frac{\frac{\partial}{\partial x} ( f ( x )) \times g ( x ) - f ( x ) \times \frac{\partial}{\partial x} ( g ( x ) )}{( g ( x ) ) ^{2}}

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

Evaluate

More Steps

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

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

\frac{\partial t}{\partial l} = \frac{\frac{π}{l ^{\frac{1}{2}}} \times g - 2 π l \times 0}{g ^{2}}

Evaluate

\frac{\partial t}{\partial l} = \frac{\frac{π g}{l ^{\frac{1}{2}}} - 2 π l \times 0}{g ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial t}{\partial l} = \frac{\frac{π g}{l ^{\frac{1}{2}}} - 0}{g ^{2}}

Removing 0 doesn't change the value,so remove it from the expression

\frac{\partial t}{\partial l} = \frac{\frac{π g}{l ^{\frac{1}{2}}}}{g ^{2}}

Evaluate

More Steps

\frac{\partial t}{\partial l} = \frac{π}{l ^{\frac{1}{2}} g}

Solution

\frac{\partial t}{\partial l} = \frac{π}{l \times g}

Function