`y = (tan^-1(x))^2` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 49 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Note:- 1) If  y = x^n ; then dy/dx = n*x^(n-1) ; where n = real number

2) If y = tan^(-1)x ; the

dy/dx = 1/{1 + (x^2)}

Now, the given function contains sub-functions, so the chain rule of differentiation is to be followed

Thus, 

 y = {tan^(-1)x}^2

Differentiating both sides w.r.t 'x' we get

dy/dx = 2*{tan^(-1)x}*[1/{1 + (x^2)}]

or, dy/dx = 2[tan^(-1)x]/[1 + (x^2)]

We’ve answered 318,984 questions. We can answer yours, too.

Ask a question