How do you differentiate #y=1/4arctan(x/4)#?
1 Answer
Jan 11, 2018
Explanation:
#•color(white)(x)d/dx(arctanx)=1/(1+x^2)#
#"differentiate using the "color(blue)"chain rule"#
#"given "y=f(g(x))" then"#
#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#
#y=1/4arctan(x/4)#
#rArrdy/dx=1/4xx1/(1+(x/4)^2)xxd/dx(x/4)#
#color(white)(rArrdy/dx)=1/4xx1/(1+(x^2/16))xx1/4#
#color(white)(rArrdy/dx)=1/16xx1/(1+(x^2/16))=1/(16+x^2)#
