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Question
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(a + bsin x)/(c + dcosx)`
Solution
Let f(x) = `(a + b sinx)/(c + d cosx)`
∴ `f'(x) = ([d/dx (a + b sinx)](c + d cos x)- (a + b sin x)d/dx(c + d cosx))/(c + dcosx)^2`
= `(b cosx(c + dcosx) - (a + b sinx)(-d sin x))/(c + d cosx)^2`
= `(bc cosx + bd cos^2 x +ad sinx + bd sin^2 x)/(c + dcosx)^2`
= `(bc cosx + ad sinx + bd(sin^2x + cos^2 x))/(c + dcosx)^2`
= `(bd cosx + ad sinx + bd)/(c + dcosx)^2`
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