Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative of Function.
\(y=sin^{-1}(3x-4x^{3})\), then \(\frac{dy}{dx}\) equals
Equation
Derivative
Algebra
Answer:\(\frac{3}{\sqrt{1-x^{2}}}\)
B.Stat Objective Problem 763
Challenges and Thrills of Pre-College Mathematics by University Press
Let x=\(sin {\theta}\)
or, \(y=sin^{-1}(3sin {\theta}-4sin^{3} {\theta})\)
or, \(y=sin^{-1}(sin3{\theta})\)=\(3{\theta}\)=\(3sin^{-1}{x}\)
or, \(\frac{dy}{dx}=\frac{3}{\sqrt{1-x^{2}}}\).
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