How do you differentiate #y=tan^-1(5x)#?
1 Answer
Oct 8, 2016
Explanation:
differentiate using the
#color(blue)"chain rule"#
#color(red)(bar(ul(|color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))...... (A)# let
#u=5xrArr(du)/(dx)=5# and
#y=tan^-1urArr(dy)/(du)=1/(1+u^2)#
#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(d/dx(tan^-1x)=1/(1+x^2))color(white)(a/a)|)))# substitute results into (A) and change u back into terms of x.
#rArrdy/dx=1/(1+u^2)xx5=5/(1+25x^2)#