Solve t = v/a - ScanMath

Simplify

t = \frac{v}{a}

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

\frac{\partial t}{\partial v} = \frac{\partial}{\partial v} (\frac{v}{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 t}{\partial v} = \frac{\frac{\partial}{\partial v} ( v ) a - v \times \frac{\partial}{\partial v} ( a )}{a ^{2}}

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

\frac{\partial t}{\partial v} = \frac{1 \times a - v \times \frac{\partial}{\partial v} ( a )}{a ^{2}}

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

\frac{\partial t}{\partial v} = \frac{1 \times a - v \times 0}{a ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial t}{\partial v} = \frac{a - v \times 0}{a ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial t}{\partial v} = \frac{a - 0}{a ^{2}}

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

\frac{\partial t}{\partial v} = \frac{a}{a ^{2}}

Solution

More Steps

\frac{\partial t}{\partial v} = \frac{1}{a}

Function