How do you differentiate #y=tan^-1(5x)#?

1 Answer
Oct 8, 2016

#dy/dx=5/(1+25x^2)#

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)#