Solve \omega =r/v

Simplify

ω = \frac{r}{v}

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

\frac{\partial ω}{\partial r} = \frac{\partial}{\partial r} (\frac{r}{v})

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

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

\frac{\partial ω}{\partial r} = \frac{1 \times v - r \times \frac{\partial}{\partial r} ( v )}{v ^{2}}

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

\frac{\partial ω}{\partial r} = \frac{1 \times v - r \times 0}{v ^{2}}

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 0 equals 0

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

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

\frac{\partial ω}{\partial r} = \frac{v}{v ^{2}}

Solution

More Steps

\frac{\partial ω}{\partial r} = \frac{1}{v}

Function