The derivative of with respect to at is

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

Problem

The derivative of tan⁡−1(1+x2−1x)\tan^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right) with respect to tan⁡−1(2x1−x21−2x2)\tan^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right) at x=0x=0 is (a) 18\frac{1}{8} (b) 14\frac{1}{4} (c) 12\frac{1}{2} (d) 11

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