Solve v=pi*d/n - ScanMath

Evaluate

v = π \times \frac{d}{n}

Multiply the terms

v = \frac{π d}{n}

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

\frac{\partial v}{\partial d} = \frac{\partial}{\partial d} (\frac{π d}{n})

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 d} = \frac{\frac{\partial}{\partial d} ( π d ) n - π d \times \frac{\partial}{\partial d} ( n )}{n ^{2}}

Evaluate

More Steps

\frac{\partial v}{\partial d} = \frac{πn - π d \times \frac{\partial}{\partial d} ( n )}{n ^{2}}

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

\frac{\partial v}{\partial d} = \frac{πn - π d \times 0}{n ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial v}{\partial d} = \frac{πn - 0}{n ^{2}}

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

\frac{\partial v}{\partial d} = \frac{πn}{n ^{2}}

Solution

More Steps

\frac{\partial v}{\partial d} = \frac{π}{n}

Function