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Q.

If y=(sinx)(sinx)sinx....∞ then dydx=

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a

y2sinx1−logy

b

y2sinx1−logy

c

y2cotx1−logy

d

y2tanx1−logy

answer is C.

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Detailed Solution

y=sinxylogy=y⋅logsinxDifferentiate both sides with respect to x1y⋅dydx=y⋅cotx+logsinxdydxdydx1y−logsinx=ycotxdydx1−y⋅logsinxy=ycotxdydx=y2cotx1−y⋅logsinx=y2⋅cotx1−logy
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