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Question

If y=(sinx)tanx, then dydxis equal to


A

sinxtanx(1+sec2xlogsinx)

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B

tanx(sinx)tanx-1cosx

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C

sinxcosxsec2xlogsinx

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D

tanx(sinx)tanx-1

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Solution

The correct option is A

sinxtanx(1+sec2xlogsinx)


Explanation for the correct option:

y=(sinx)tanx

Taking log both sides:

logy=logsinxtanxlogy=tanxlog(sinx)

Using Product Rule, Differentiating with respect to x both sides:

1ydydx=sec2x×log(sinx)+tanx×1sinx×cosx1ydydx=sec2xlog(sinx)+tanx×cotx1ydydx=sec2xlog(sinx)+1dydx=y(1+sec2xlog(sinx))dydx=sinxtanx(1+sec2xlogsinx)

Hence, Option (A) is the correct answer.


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