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Differential Calculus> Differentiate y=Sin -1 (sqrt x X sqrt (1-...

question mark

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

Aditya Maniklal Tapase , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 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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