Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative of Function.

Derivative of Function (B.Stat Objective Question )


\(y=sin^{-1}(3x-4x^{3})\), then \(\frac{dy}{dx}\) equals

  • 3x
  • \(\frac{3}{\sqrt{1-x^{2}}}\)
  • 3
  • none of the foregoing expressions

Key Concepts


Equation

Derivative

Algebra

Check the Answer


But try the problem first…

Answer:\(\frac{3}{\sqrt{1-x^{2}}}\)

Source
Suggested Reading

B.Stat Objective Problem 763

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

Let x=\(sin {\theta}\)

or, \(y=sin^{-1}(3sin {\theta}-4sin^{3} {\theta})\)

Second Hint

or, \(y=sin^{-1}(sin3{\theta})\)=\(3{\theta}\)=\(3sin^{-1}{x}\)

Final Step

or, \(\frac{dy}{dx}=\frac{3}{\sqrt{1-x^{2}}}\).

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