Solve P=F/A - ScanMath

Simplify

P = \frac{F}{A}

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

\frac{\partial P}{\partial F} = \frac{\partial}{\partial F} (\frac{F}{A})

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 P}{\partial F} = \frac{\frac{\partial}{\partial F} ( F ) A - F \times \frac{\partial}{\partial F} ( A )}{A ^{2}}

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

\frac{\partial P}{\partial F} = \frac{1 \times A - F \times \frac{\partial}{\partial F} ( A )}{A ^{2}}

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

\frac{\partial P}{\partial F} = \frac{1 \times A - F \times 0}{A ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial P}{\partial F} = \frac{A - F \times 0}{A ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial P}{\partial F} = \frac{A - 0}{A ^{2}}

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

\frac{\partial P}{\partial F} = \frac{A}{A ^{2}}

Solution

More Steps

\frac{\partial P}{\partial F} = \frac{1}{A}

Function