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

##### 1 Answer

Feb 4, 2018

# 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) #