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Question

If y=tanx+tanx+tanx+to , then dydx=psec2xqy+r, p,q,rN. Find the minimum positive value of p+q+r.

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Solution

Square both sides the given equation,
y2=tanx+y
Now differentiate both sides with respect to x
2ydydx=sec2x+dydx
(2y1)dydx=sec2x
dydx=sec2x2y1
So, p=1,q=2,r=1
p+q+r=2

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