How do you differentiate # x/(e^(2x))#?
1 Answer
May 31, 2016
Explanation:
differentiate using the
#color(blue)"quotient and chain rules"# f(x) = g(x).h(x) then
#f'(x)=(h(x).g'(x)-g(x).h'(x))/(h(x)^2#
#d/dx(f(g(x))=f'(g(x)).g'(x)#
#"-------------------------------------------------------------"#
#g(x)=xrArrg'(x)=1#
#h(x)=e^(2x)rArrh'(x)=e^(2x).2=2e^(2x)#
#"------------------------------------------------------------"#
Substitute these values into f'(x) in the quotient rule
#f'(x)=(e^(2x).1-x.2e^(2x))/(e^(2x))^2=(e^(2x)-2xe^(2x))/e^(4x)#
#=(e^(2x)(1-2x))/e^(4x)=(1-2x)/e^(2x)#
