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प्रश्न
`(x^2 cos pi/4)/sinx`
उत्तर
`d/(dx) ((x^2 cos pi/4)/sinx) = cos pi/4 * d/(dx) (x^2/sinx)`
= `(1/sqrt(2) [sin x * d/(dx) (x^2) - x^2 * d/(dx) (sin x)])/(sin^2x)` ......[Using quotient rule]
= `1/sqrt(2) [(sin x * 2x - x^2 cos x)/(sin^2x)]`
= `1/sqrt(2) [(2x)/sinx - (x^2 cosx)/(sin^2x)]`
= `1/sqrt(2) [2x "cosec" x = x^2 cot x "cosec" x]`
= `x/sqrt(2) "cosec" x [2 - x cot x]`
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