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Question
Find the derivative of `cosx/(1 + sinx)`
Solution
Let y = `cosx/(1 + sinx)`
Differentiating both sides with respects to x, we get
`(dy)/(dx) = d/(dx) cosx/(1 + sinx)`
= `((1 + sin x) d/(dx) (cosx) - cos x d/(dx) (1 + sin x))/(1 + sinx)^2`
= `((1 + sinx)(- sinx) - cos x (cosx))/(1 + sin x)^2`
= `(- sin x - sin^2x - cos^2x)/(1 + sin x)^2`
= `(-(1 + sinx))/(1 + sin x)^2`
= `(-1)/(1 + sin x)`
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If `y = 1 + x/(1!) + x^2/(2!) + x^3/(3!) + ...,` then `(dy)/(dx)` = ______.
