Solve f=m1m^2/r^2

Evaluate

f = m (1 \times \frac{m ^{2}}{r ^{2}})

Remove the parentheses

f = m \times 1 \times \frac{m ^{2}}{r ^{2}}

Multiply the terms

More Steps

f = \frac{m ^{3}}{r ^{2}}

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

\frac{\partial f}{\partial m} = \frac{\partial}{\partial m} (\frac{m ^{3}}{r ^{2}})

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 f}{\partial m} = \frac{\frac{\partial}{\partial m} ( m ^{3} ) r ^{2} - m ^{3} \times \frac{\partial}{\partial m} ( r ^{2} )}{( r ^{2} ) ^{2}}

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

\frac{\partial f}{\partial m} = \frac{3 m ^{2} r ^{2} - m ^{3} \times \frac{\partial}{\partial m} ( r ^{2} )}{( r ^{2} ) ^{2}}

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

\frac{\partial f}{\partial m} = \frac{3 m ^{2} r ^{2} - m ^{3} \times 0}{( r ^{2} ) ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial f}{\partial m} = \frac{3 m ^{2} r ^{2} - 0}{( r ^{2} ) ^{2}}

Evaluate

More Steps

\frac{\partial f}{\partial m} = \frac{3 m ^{2} r ^{2} - 0}{r ^{4}}

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

\frac{\partial f}{\partial m} = \frac{3 m ^{2} r ^{2}}{r ^{4}}

Solution

More Steps

\frac{\partial f}{\partial m} = \frac{3 m ^{2}}{r ^{2}}

Function