How do you differentiate #f(x) = Tan^(-1) (x/2)#?
1 Answer
Mar 23, 2018
Explanation:
#•color(white)(x)d/dx(tan^-1x)=1/(1+x^2)#
#"differentiate using the "color(blue)"chain rule"#
#"Given "f(x)=g(h(x))" then"#
#f'(x)=g'(h(x))xxh'(x)larrcolor(blue)"chain rule"#
#f(x)=tan^-1(x/2)#
#rArrf'(x)=1/(1+(x/2)^2)xxd/dx(1/2x)#
#color(white)(rArrf'(x))=(1/2)/(1+x^2/4)xx4/4#
#color(white)(rArrf'(x))=2/(4+x^2)#