How do you find the derivative of #y(x)= (9x)/(x-3)^2#?
1 Answer
Aug 7, 2017
Explanation:
#"one way is to differentiate using the quotient rule"#
#"given "y=(g(x))/(h(x))" then"#
#dy/dx=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#
#g(x)=9xrArrg'(x)=9#
#h(x)=(x-3)^2rArrh'(x)=2(x-3)#
#rArrdy/dx=((x-3)^2 .9-9x.2(x-3))/(x-3)^4#
#color(white)(rArrdy/dx)=((x-3)(9x-27-18x))/(x-3)^4#
#color(white)(rArrdy/dx)=-(9x+27)/(x-3)^3#
