A Level

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

Problem

If y=(1+1x)xy = \left(1 + \frac{1}{x}\right)^x , then dydx=\frac{dy}{dx} = (a) (1+1x)x[log⁡(1+1x)−11+x]\left(1 + \frac{1}{x}\right)^x \left[ \log\left(1 + \frac{1}{x}\right) - \frac{1}{1 + x} \right] (b) (1+1x)x[log⁡(1+1x)]\left(1 + \frac{1}{x}\right)^x \left[ \log\left(1 + \frac{1}{x}\right) \right] (c) (x+1x)x[log⁡(x−1)−xx+1]\left(x + \frac{1}{x}\right)^x \left[ \log(x - 1) - \frac{x}{x + 1} \right] (d) (1+1x)x[log⁡(1+1x)+11+x]\left(1 + \frac{1}{x}\right)^x \left[ \log\left(1 + \frac{1}{x}\right) + \frac{1}{1 + x} \right]

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