Solve t=2h/g - ScanMath

Evaluate

t = 2 \times \frac{h}{g}

Multiply the terms

t = \frac{2 h}{g}

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

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

Evaluate

More Steps

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

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

\frac{\partial t}{\partial h} = \frac{2 g - 2 h \times 0}{g ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial t}{\partial h} = \frac{2 g - 0}{g ^{2}}

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

\frac{\partial t}{\partial h} = \frac{2 g}{g ^{2}}

Solution

More Steps

\frac{\partial t}{\partial h} = \frac{2}{g}

Function