What is the derivative of #tan(1/x)#?
1 Answer
Jul 15, 2017
Explanation:
#"differentiate using the "color(blue)"chain rule"#
#d/dx(tanx)=sec^2x#
#•color(white)(x)d/dx(tan(f(x)))=sec^2(f(x))xxf'(x)#
#f(x)=1/x=x^-1rArrf'(x)=-1x^-2=-1/x^2#
#rArrd/dx(tan(1/x))=sec^2(1/x)xx-1/x^2#
#=-1/x^2sec^2(1/x)#
