What is the derivative of #sin (x/2)#?
1 Answer
Jul 13, 2016
Explanation:
Differentiate using the
#color(blue)"chain rule"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(f(g(x)))=f'(g(x))g'(x))color(white)(a/a)|))) ........ (A)#
#f(g(x))=sin(x/2)rArrf'(g(x))=cos(x/2)# and
#g(x)=x/2=1/2xrArrg'(x)=1/2#
#"------------------------------------------------------"#
Substitute rhese values into (A)
#rArrf'(g(x))=cos(x/2)xx1/2=1/2cos(x/2)#
