Given , which of the following is…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Given h(x)=(x2+1)3cos⁡(x)h(x)=(x^{2}+1)^{3}\cos(\sqrt{x}), which of the following is h′(x)h'(x)? (a) 6x(x2+1)2cos⁡(x)−(x2+1)3sin⁡(x)6x(x^{2}+1)^{2}\cos(\sqrt{x})-(x^{2}+1)^{3}\sin(\sqrt{x}) (b) 6x(x2+1)2cos⁡(x)−(x2+1)3sin⁡(x)2x6x(x^{2}+1)^{2}\cos(\sqrt{x})-\dfrac{(x^{2}+1)^{3}\sin(\sqrt{x})}{2\sqrt{x}} (c) 6x(x2+1)2cos⁡(x)−(x2+1)3cos⁡(x)2x6x(x^{2}+1)^{2}\cos(\sqrt{x})-\dfrac{(x^{2}+1)^{3}\cos(\sqrt{x})}{2\sqrt{x}} (d) 3(x2+1)2cos⁡(x)−(x2+1)3sin⁡(x)2x3(x^{2}+1)^{2}\cos(\sqrt{x})-\dfrac{(x^{2}+1)^{3}\sin(\sqrt{x})}{2\sqrt{x}}

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