Solve r= 3v : p - ScanMath

Evaluate

r = 3 v \div p

Rewrite the expression

r = \frac{3 v}{p}

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

\frac{\partial r}{\partial v} = \frac{\partial}{\partial v} (\frac{3 v}{p})

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 r}{\partial v} = \frac{\frac{\partial}{\partial v} ( 3 v ) p - 3 v \times \frac{\partial}{\partial v} ( p )}{p ^{2}}

Evaluate

More Steps

\frac{\partial r}{\partial v} = \frac{3 p - 3 v \times \frac{\partial}{\partial v} ( p )}{p ^{2}}

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

\frac{\partial r}{\partial v} = \frac{3 p - 3 v \times 0}{p ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial r}{\partial v} = \frac{3 p - 0}{p ^{2}}

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

\frac{\partial r}{\partial v} = \frac{3 p}{p ^{2}}

Solution

More Steps

\frac{\partial r}{\partial v} = \frac{3}{p}

Function