What is the derivative of #y=x/(5-3x)#?

1 Answer
Mar 15, 2018

#5/(5-3x)^2#

Explanation:

For this we have to use the quotient rule which is,
#(f/g)prime=(fprime*g-f*gprime)/g^2#

Where
#f=x#
#fprime=1#
#g=(5-3x)#
#gprime=-3#

So now we plug it into the formula
#((1)*(5-3x)-[x(-3)])/(5-3x)^2#

Which simplifies to
#((5-3x)-(-3x))/(5-3x)^2#

#(5-3x+3x)/(5-3x)^2#

#5/(5-3x)^2# which is the answer.