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# Derivative of Function Problem | TOMATO BStat Objective 757

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

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

Equation

Derivative

Algebra

## Check the Answer

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

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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