Solve B=P/R - ScanMath

Simplify

B = \frac{P}{R}

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

\frac{\partial B}{\partial P} = \frac{\partial}{\partial P} (\frac{P}{R})

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 B}{\partial P} = \frac{\frac{\partial}{\partial P} ( P ) R - P \times \frac{\partial}{\partial P} ( R )}{R ^{2}}

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

\frac{\partial B}{\partial P} = \frac{1 \times R - P \times \frac{\partial}{\partial P} ( R )}{R ^{2}}

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

\frac{\partial B}{\partial P} = \frac{1 \times R - P \times 0}{R ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial B}{\partial P} = \frac{R - P \times 0}{R ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial B}{\partial P} = \frac{R - 0}{R ^{2}}

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

\frac{\partial B}{\partial P} = \frac{R}{R ^{2}}

Solution

More Steps

\frac{\partial B}{\partial P} = \frac{1}{R}

Function