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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):
`cos x/(1 + sin x)`
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Solution
Let f(x) = `(cos x)/(1 + sin x)`
By quotient rule,
f'(x) = `((1 + sin x)d/dx(cos x) - (cos x)d/dx (1 + sin x))/(1 + sin x)^2`
= `((1 + sin x) (-sin x) - (cos x) (cos x))/(1 + sin x)^2`
= `(-sin x - sin^2 x - cos^2 x)/(1 + sin x)^2`
= `(-sin x - (sin^2 x - cos^2 x))/(1 + sin x)^2`
= `(-sin x - 1)/(1 + sin x)^2`
= `(-(1 + sin x))/(1 + sin x)^2`
= `(-1 )/((1 + sin x))`
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