Please solve urgently.... Correct Answer is: 1/(x * (x + 1)^(1/2)) + 1/( 2(x)^(1/2) * (x + 1)^(3/2))

L e t y = \log \frac{\sqrt{(x + 1)} - 1}{\sqrt{(x + 1)} + 1} + \frac{\sqrt{x}}{\sqrt{x + 1}} U s e \log \frac{m}{n} = \log m - \log n y = \log (\sqrt{x + 1} - 1) - \log (\sqrt{x + 1} + 1) + \frac{\sqrt{x}}{\sqrt{x + 1}} \frac{d y}{d x} = \frac{d}{d x} \log (\sqrt{x + 1} - 1) - \frac{d}{d x} \log (\sqrt{x + 1} + 1) + \frac{d}{d x} (\frac{\sqrt{x}}{\sqrt{x + 1}}) \frac{d y}{d x} = (\frac{1}{\sqrt{x + 1} - 1}) \frac{d}{d x} (\sqrt{x + 1} - 1) - (\frac{1}{\sqrt{x + 1} + 1}) \frac{d}{d x} (\sqrt{x + 1} + 1) + (\frac{\sqrt{x + 1} \frac{d}{d x} \sqrt{x} - \sqrt{x} \frac{d}{d x} \sqrt{x + 1}}{{(\sqrt{x + 1})}^{2}}) \frac{d y}{d x} = (\frac{1}{\sqrt{x + 1} - 1}) (\frac{1}{2 \sqrt{x + 1}}) - (\frac{1}{\sqrt{x + 1} + 1}) (\frac{1}{2 \sqrt{x + 1}}) + (\frac{\sqrt{x + 1} (\frac{1}{2 \sqrt{x}}) - \sqrt{x} (\frac{1}{2 \sqrt{x + 1}})}{{(\sqrt{x + 1})}^{2}}) \frac{d y}{d x} = (\frac{1}{2 \sqrt{x + 1}}) (\frac{1}{\sqrt{x + 1} - 1} - \frac{1}{\sqrt{x + 1} + 1}) + (\frac{(\frac{{(\sqrt{x + 1})}^{2} - {(\sqrt{x})}^{2}}{2 \sqrt{x + 1} \sqrt{x}})}{{(\sqrt{x + 1})}^{2}}) \frac{d y}{d x} = (\frac{1}{2 \sqrt{x + 1}}) (\frac{\sqrt{x + 1} + 1 - (\sqrt{x + 1} - 1)}{(\sqrt{x + 1} - 1) (\sqrt{x + 1} + 1)}) + (\frac{(\frac{(x + 1) - (x)}{2 \sqrt{x + 1} \sqrt{x}})}{x + 1}) \frac{d y}{d x} = (\frac{1}{2 \sqrt{x + 1}}) (\frac{2}{{(\sqrt{x + 1})}^{2} - 1^{2}}) + (\frac{(\frac{1}{2 \sqrt{x + 1} \sqrt{x}})}{x + 1}) \frac{d y}{d x} = (\frac{1}{2 \sqrt{x + 1}}) (\frac{2}{(x + 1) - 1}) + (\frac{1}{2 {(x + 1)}^{\frac{3}{2}} \sqrt{x}}) \frac{d y}{d x} = (\frac{1}{2 \sqrt{x + 1}}) (\frac{2}{x}) + (\frac{1}{2 {(x + 1)}^{\frac{3}{2}} \sqrt{x}}) \frac{d y}{d x} = \frac{1}{x \sqrt{x + 1}} + \frac{1}{2 {(x + 1)}^{\frac{3}{2}} \sqrt{x}}

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