26. If y= tan-"{1 + x2 - x} find dy...
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26. If y= tan-"{1 + x2 - x} find dy

11th - 12th Class
Maths
Solution
175
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( begin{aligned} y &=tan ^{-1}{sqrt{1+x^{2}}-x} frac{operatorname{dy}}{d x}=frac{1}{1+(sqrt{1+x^{2}-x})^{2}}left[frac{2 x}{2 sqrt{1+x^{2}}}-1right] &=frac{x-sqrt{1+x^{2}}}{sqrt{1+x^{2}}left(1+left(1+x^{2}right)+x^{2}-2 x sqrt{1+x^{2}}right)} &=frac{x-sqrt{1+x^{2}}}{2 sqrt{1+x^{2}}left(1+x^{2}-x sqrt{1+x^{2}}right)} end{aligned} )
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