What is the derivative of this function #tan^-1(5x)#?
1 Answer
Aug 20, 2016
Explanation:
differentiate using the
#color(blue)"chain rule"#
#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(tan^-1 x)=1/(1+x^2))color(white)(a/a)|)))# let
#u=5xrArr(du)/(dx)=5# and
#y=tan^-1 urArr(dy)/(du)=1/(1+u^2# Substitute these values into (A) and convert u back into x.
#rArrdy/dx=1/(1+(5x)^2) .5=5/(1+25x^2)#