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prove-that-the-differentiation-of-1-x-2-1-x-2-1-x-2-1-x-2-with-respect-to-1-x-4-is-1-x-4-x-6-




Question Number 18905 by Arnab Maiti last updated on 01/Aug/17
prove that the differentiation  of(((√(1+x^2 ))−(√(1−x^2 )))/( (√(1+x^2 ))+(√(1−x^2 ))))  with respect  to (√(1−x^4 ))  is  ((√(1−x^4 ))/x^6 )
$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{differentiation} \\ $$$$\mathrm{of}\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\:\mathrm{with}\:\mathrm{respect} \\ $$$$\mathrm{to}\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }\:\:\mathrm{is}\:\:\frac{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}{\mathrm{x}^{\mathrm{6}} } \\ $$

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