Solve r=u^2/p - ScanMath

Simplify

r = \frac{u ^{2}}{p}

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

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

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

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

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

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

Any expression multiplied by 0 equals 0

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

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

\frac{\partial r}{\partial u} = \frac{2 u p}{p ^{2}}

Solution

More Steps

\frac{\partial r}{\partial u} = \frac{2 u}{p}

Function