If f x = x x + x x + sin ⁡ π x , where [·] and {·} represent the greatest integer function and the fractional part function respectively, then f ' 7 2 is equal to

Question

If f x = x x + x x + sin ⁡ π x , where [·] and {·} represent the greatest integer function and the fractional part function respectively, then f ' 7 2 is equal to, 3 l n 3 + π 4, 3 l n 3 + 3 π 4, 3 l n 3 + π + 3 4, 3 l n 3 + 3 4

MARKS App · Accepted Answer

f x = x x + x x + sin ⁡ π x f x = 3 x - 3 + x - 3 3 + sin ⁡ π x , x ∈ 3 , 4 f ' x = 3 x - 3 ln ⁡ 3 + 3 x - 3 2 + π cos ⁡ π x ∴ f ' 7 2 = 3 l n 3 + 3 4

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