Question

What is the derivative of `(3y)/(2x)`?

Answer 1

`d/dx( (3y)/(2x) ) = ( 3 ( x dy/dx - y ) )/ (2x^2)`

Explanation:

Applying linearity and the quotient rule we have:

`d/dx( (3y)/(2x) ) = 3/2 \ d/dx( y/x )`

`" " = 3/2 \ ( (x)(d/dx y) - (y)(d/dx x) ) / (x)^2`

`" " = 3/2 \ ( x dy/dx - y ) / (x^2)`
`" " = ( 3 ( x dy/dx - y ) )/ (2x^2)`