Solve f = n/s - ScanMath

Simplify

f = \frac{n}{s}

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

\frac{\partial f}{\partial n} = \frac{\partial}{\partial n} (\frac{n}{s})

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

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

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

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

\frac{\partial f}{\partial n} = \frac{1 \times s - n \times 0}{s ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial f}{\partial n} = \frac{s - n \times 0}{s ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial f}{\partial n} = \frac{s - 0}{s ^{2}}

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

\frac{\partial f}{\partial n} = \frac{s}{s ^{2}}

Solution

More Steps

\frac{\partial f}{\partial n} = \frac{1}{s}

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