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cos–¹(x/x+1) |
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Answer» \(\frac{d}{dx}cos^{-1}(\frac{x}{x+1})=\cfrac{-1}{\sqrt{1-(\frac{x}{x+1})^2}}\frac{d}{dx}(\frac{x}{x+1})\) = \(\frac{-(x+1)}{\sqrt{(x+1)^2-x^2}}\times\frac{(x+1).1-x(1)}{(x+1)^2}\) = \(\frac{-(x+1)}{\sqrt{2x+1}}\times\frac1{(x+1)^2}\) = \(\frac{-1}{\sqrt{2x+1}(x+1)}\) |
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