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Question
`(a + b sin x)/(c + d cos x)`
Solution
`d/(dx) ((a + b sin x)/(c + d cos x))`
= `((c + d cos x) * d/(dx) (a + b sin x) - (a + b sin x) d/(dx) (c + d + cos x))/(c + d cos x)^2`
= `((c + d cos x) (b cos x) - (a + b sin x)(- d sin x))/(c + d cos x)^2` .....[Using quotient rule]
= `(cb cos x + bd cos^2x + ad sin x + bd sin^2x)/(c + d cos x)^2`
= `(cb cos x + ad sin x + bd (cos^2x + sin^2x))/(c + d cos x)^2`
= `(cb cos x + ad sin x + bd)/(c + d cos x)^2`
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