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Question
`(x^5 - cosx)/sinx`
Solution
`d/(dx) ((x^5 - cos x)/sinx) = (sin x * d/(dx) (x^5 - cos x) - (x^5 - cos x) * d/(dx) (sin x))/(sin^2x)`
= `(sin x(5x^4 + sin x) - (x^5 - cos x)(cosx))/(sin^2x)` ....[Using quotient rule]
= `(5x^4 * sin x + sin^2x - x^5 cos x + cos^2x)/(sin^2x)`
= `(5x^4 sinx - x^5 cosx + (sin^2x + cos^2x))/(sin^2x)`
= `(5x^4 sin x - x^5 cos x + 1)/(sin^2x)`
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