Solve f = \frac{r}{n - 1}

Simplify

f = \frac{r}{n - 1}

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

\frac{\partial f}{\partial r} = \frac{\partial}{\partial r} (\frac{r}{n - 1})

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

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

\frac{\partial f}{\partial r} = \frac{1 \times ( n - 1 ) - r \times \frac{\partial}{\partial r} ( n - 1 )}{( n - 1 ) ^{2}}

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

\frac{\partial f}{\partial r} = \frac{1 \times ( n - 1 ) - r \times 0}{( n - 1 ) ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial f}{\partial r} = \frac{n - 1 - r \times 0}{( n - 1 ) ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial f}{\partial r} = \frac{n - 1 - 0}{( n - 1 ) ^{2}}

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

\frac{\partial f}{\partial r} = \frac{n - 1}{( n - 1 ) ^{2}}

Solution

More Steps

\frac{\partial f}{\partial r} = \frac{1}{n - 1}

Function