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

1 Answer
Jim G.
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)

Related questions
See all questions in Differentiating Inverse Trigonometric Functions
Impact of this question
4897 views around the world
You can reuse this answer
Creative Commons License