Solve a=2s/t^2 - ScanMath

Evaluate

a = 2 \times \frac{s}{t ^{2}}

Multiply the terms

a = \frac{2 s}{t ^{2}}

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

\frac{\partial a}{\partial s} = \frac{\partial}{\partial s} (\frac{2 s}{t ^{2}})

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

Evaluate

More Steps

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

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

\frac{\partial a}{\partial s} = \frac{2 t ^{2} - 2 s \times 0}{( t ^{2} ) ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial a}{\partial s} = \frac{2 t ^{2} - 0}{( t ^{2} ) ^{2}}

Evaluate

More Steps

\frac{\partial a}{\partial s} = \frac{2 t ^{2} - 0}{t ^{4}}

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

\frac{\partial a}{\partial s} = \frac{2 t ^{2}}{t ^{4}}

Solution

More Steps

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

Function