Solve v = \frac{q}{a_p}

Simplify

v = \frac{q}{a _{p}}

Find the first partial derivative by treating the variable a_{p} as a constant and differentiating with respect to q

\frac{\partial v}{\partial q} = \frac{\partial}{\partial q} (\frac{q}{a _{p}})

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 v}{\partial q} = \frac{\frac{\partial}{\partial q} ( q ) a _{p} - q \times \frac{\partial}{\partial q} ( a _{p} )}{a _{p}^{2}}

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

\frac{\partial v}{\partial q} = \frac{1 \times a _{p} - q \times \frac{\partial}{\partial q} ( a _{p} )}{a _{p}^{2}}

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

\frac{\partial v}{\partial q} = \frac{1 \times a _{p} - q \times 0}{a _{p}^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial v}{\partial q} = \frac{a _{p} - q \times 0}{a _{p}^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial v}{\partial q} = \frac{a _{p} - 0}{a _{p}^{2}}

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

\frac{\partial v}{\partial q} = \frac{a _{p}}{a _{p}^{2}}

Solution

More Steps

\frac{\partial v}{\partial q} = \frac{1}{a _{p}}

Function