Let . Which of the following is equivalent to…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let h(x)=tan⁡(2x)cot⁡(3x)h(x)=\dfrac{\tan(2x)}{\cot(3x)}. Which of the following is equivalent to h′(x)h'(x)? (a) 2sec⁡2(2x)cot⁡(3x)−3tan⁡(2x)csc⁡2(3x)cot⁡2(3x)\dfrac{2\sec^{2}(2x)\cot(3x)-3\tan(2x)\csc^{2}(3x)}{\cot^{2}(3x)} (b) 2sec⁡2(2x)cot⁡(3x)+3tan⁡(2x)csc⁡2(3x)cot⁡2(3x)\dfrac{2\sec^{2}(2x)\cot(3x)+3\tan(2x)\csc^{2}(3x)}{\cot^{2}(3x)} (c) 6sec⁡2(2x)csc⁡2(3x)cot⁡2(3x)\dfrac{6\sec^{2}(2x)\csc^{2}(3x)}{\cot^{2}(3x)} (d) sec⁡2(2x)cot⁡(3x)+3tan⁡(2x)csc⁡2(3x)cot⁡2(3x)\dfrac{\sec^{2}(2x)\cot(3x)+3\tan(2x)\csc^{2}(3x)}{\cot^{2}(3x)}

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