Mathematics

Problem

Let

y=(x^{2}+1)^{\tan^{-1}x}, \qquad x>0.

Answer the following questions. a. (i) Differentiate

y

with respect to

x

and simplify your result. b. (ii) Evaluate

\dfrac{dy}{dx}

x=1

. c. (iii) Using your answer from part (i), find the value of

\dfrac{d^{2}y}{dx^{2}}

x=1