Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative of Function.
If f(x)=(sinx)(sin2x).....(sinnx), then f'(x) is
Equation
Derivative
Algebra
Answer:\(\sum_{k=1}^{n}(kcot{kx})(f(x)\).
B.Stat Objective Problem 757
Challenges and Thrills of Pre-College Mathematics by University Press
f(x)=(sinx)(sin2x).....(sinnx)
or, \(f'(x)=cosx(sin2x).......(sinnx)\)
+\(2sinxcos2x....(sinnx)+.....+n(sinx)(sin2x)....(cosnx)\)
=\(\sum_{k=1}^{n}k\frac{coskx}{sinkx}f(x)\)
=\(\sum_{k=1}^{n}kcot{kx}f(x)\).
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