Consider the function defined for all real .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the function g(x)=sin⁡x1+2xg(x)=\dfrac{\sin x}{1+2x} defined for all real xx. (i) Find g′(x)g'(x). (ii) Evaluate g′ ⁣(π6)g'\!\left(\dfrac{\pi}{6}\right). (iii) Using the value obtained in part (ii), approximate the change in g(x)g(x) when xx increases from π6\dfrac{\pi}{6} to π6+0.01\dfrac{\pi}{6}+0.01.

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