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Question
Differentiate the following:
y = `(sin^2x)/cos x`
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Solution
y = `(sin^2x)/cos x`
`("d"y)/("d"x) = (cosx(2sinx cos x) - sin^2x xx - sin x)/(cos x)^2`
`("d"y)/("d"x) = (2sinx cos^2x + sin^3x)/(cos^2x)`
= `sin x ((2 cos^2 x + sin^2 x))/(cos^2x)`
= `sin x((2cos2x)/(cos^2x) + (sin2x)/(cos2x))`
= sin x(2 + tan2x)
= sin x(1 + 1 + tan2x)
`("d"y)/("d"x)` = sin x(1 + sec2 x)
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