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

Derivative of Function Problem (B.Stat Objective Question )


If f(x)=(sinx)(sin2x)…..(sinnx), then f'(x) is

  • \(\sum_{k=1}^{n}(kcos{kx})f(x)\)
  • \(\sum_{k=1}^{n}(kcot{kx})f(x)\)
  • \((cosx)(2cos2x)(3cos3x)…..(ncosnx)\)
  • \(\sum_{k=1}^{n}(kcos{kx})(sin{kx})\)

Key Concepts


Equation

Derivative

Algebra

Check the Answer


But try the problem first…

Answer:\(\sum_{k=1}^{n}(kcot{kx})(f(x)\).

Source
Suggested Reading

B.Stat Objective Problem 757

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

f(x)=(sinx)(sin2x)…..(sinnx)

or, \(f'(x)=cosx(sin2x)…….(sinnx)\)

+\(2sinxcos2x….(sinnx)+…..+n(sinx)(sin2x)….(cosnx)\)

Second Hint

=\(\sum_{k=1}^{n}k\frac{coskx}{sinkx}f(x)\)

Final Step

=\(\sum_{k=1}^{n}kcot{kx}f(x)\).

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