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Question

If y=sinx+sinx+sinx+to, then dydx is

A
cosx1+2y
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B
sinx12y
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C
cosx12y
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D
cosx2y1
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Solution

The correct option is D cosx2y1
We have
y=sinx+sinx+sinx+to
The given series may be written as
y=sinx+y
Squaring both the sides, we get
y2=sinx+y
Differentiating both sides w.r.t. x
2ydydx=cosx+dydx
2ydydxdydx=cosx
dydx(2y1)=cosx
dydx=cosx2y1

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