Let g(x)= (2x^ 2 -3x) x x^ 2 +1 + x x 2x-1

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let g(x)=(2x2−3x)sin⁡xx2+1+xcos⁡x2x−1.g(x)=\frac{(2x^{2}-3x)\sin x}{x^{2}+1}+\frac{x\cos x}{2x-1}. (i) Find g′(x)g'(x), showing each major algebraic step. (ii) Factorise your answer to part (i) so that no trigonometric function appears more than once in any term. (iii) Using the simplified form obtained in part (ii), evaluate g′(0)g'(0).

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