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Differentiate y=Sin -1 (sqrt x X sqrt (1-x) + x X sqrt (1-x 2 )

Differentiate
y=Sin-1(sqrt x X sqrt (1-x) + x X sqrt (1-x2)

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:Hello student, please find answer to your question
y = sin^{-1}(\sqrt{x}\sqrt{1-x} + \sqrt{x}\sqrt{1-x^{2}})
y = sin^{-1}(\sqrt{x-x^{2}} + \sqrt{x-x^{3}})
y = sin^{-1}(\sqrt{x-x^{2}} + \sqrt{(x-x^{2})(1+x)})
y = sin^{-1}(\sqrt{x-x^{2}} (1+\sqrt{1+x}))
\frac{dy}{dx} = \frac{1}{\sqrt{1-((x-x^{2})(1+\sqrt{1+x})^{2})}}.\frac{1}{2}[\frac{1-2x}{\sqrt{x-x^{2}}}+\frac{1-3x^{2}}{\sqrt{x-x^{3}}}]
\frac{dy}{dx} = \frac{1}{2}.\frac{[\frac{1-2x}{\sqrt{x-x^{2}}}+\frac{1-3x^{2}}{\sqrt{x-x^{3}}}]}{\sqrt{1-((x-x^{2})(1+\sqrt{1+x})^{2})}}

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