Let y=(x^ 2 +1)^ ^ -1 x

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let y=(x2+1)tan⁡−1x,x>0.y=(x^{2}+1)^{\tan^{-1}x}, \qquad x>0. Answer the following questions. (i) Differentiate yy with respect to xx and simplify your result. (ii) Evaluate dydx\dfrac{dy}{dx} at x=1x=1. (iii) Using your answer from part (i), find the value of d2ydx2\dfrac{d^{2}y}{dx^{2}} at x=1x=1.

Related theory

Browse the problem library