How do you differentiate #f(x)=sin(1/(3x-1))# using the chain rule?
1 Answer
May 14, 2016
Explanation:
differentiate using the
#color(blue)" chain rule"#
#d/dx[f(g(x))]=f'(g(x)).g'(x)color(red)" (A)"#
#"-------------------------------------------"#
#f(g(x))=sin(1/(3x-1))rArrf'(g(x))=cos(1/(3x-1))# and
#g(x)=1/(3x-1)=(3x-1)^-1 #
#rArrg'(x)=-1(3x-1)^-2 .3=-3(3x-1)^-2=(-3)/(3x-1)^2#
#"-----------------------------------------------------"#
Substitute these values into#color(red)" (A)"#
#f'(x)=cos(1/(3x-1))xx(-3)/(3x-1)^2=(-3cos(1/(3x-1)))/(3x-1)^2#
