Solve v = \frac{2\pi r}{t}

Simplify

v = \frac{2 π r}{t}

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

\frac{\partial v}{\partial r} = \frac{\partial}{\partial r} (\frac{2 π r}{t})

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 v}{\partial r} = \frac{\frac{\partial}{\partial r} ( 2 π r ) t - 2 π r \times \frac{\partial}{\partial r} ( t )}{t ^{2}}

Evaluate

More Steps

\frac{\partial v}{\partial r} = \frac{2 π t - 2 π r \times \frac{\partial}{\partial r} ( t )}{t ^{2}}

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

\frac{\partial v}{\partial r} = \frac{2 π t - 2 π r \times 0}{t ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial v}{\partial r} = \frac{2 π t - 0}{t ^{2}}

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

\frac{\partial v}{\partial r} = \frac{2 π t}{t ^{2}}

Solution

More Steps

\frac{\partial v}{\partial r} = \frac{2 π}{t}

Function