Solve s=v:t - ScanMath

Evaluate

s = v \div t

Rewrite the expression

s = \frac{v}{t}

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

\frac{\partial s}{\partial v} = \frac{\partial}{\partial v} (\frac{v}{t})

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

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

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

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

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 0 equals 0

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

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

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

Solution

More Steps

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

Function