If y=x+1x2−xxx+x+x+115 (3cos2x−5)cos3x then 32 y1(π/6) is equal to

Y=(x+1)x((x)3−1)x((x)2+x+1) + 115(3cos5x−5cos3x) y=(x+1)(x−1)+15cos5x −13cos3x y1=1−cos4x sinx +cos2xsinx y1(π6)=3532 ⇒32y1(π6)=35

If y=x+1x2−xxx+x+x+115 (3cos2x−5)cos3x then 32 y1(π/6) is equal to

Y=(x+1)x((x)3−1)x((x)2+x+1) + 115(3cos5x−5cos3x) y=(x+1)(x−1)+15cos5x −13cos3x y1=1−cos4x sinx +cos2xsinx y1(π6)=3532 ⇒32y1(π6)=35

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If $y = \frac{(\sqrt{x} + 1) (x^{2} - \sqrt{x})}{x \sqrt{x} + x + \sqrt{x}} + \frac{1}{15}$ $(3 \cos^{2} x - 5) \cos^{3} x$ then $32 y^{1} (π / 6)$ is equal to

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Detailed Solution

$Y = \frac{(\sqrt{x} + 1) \sqrt{x} ({(\sqrt{x})}^{3} - 1)}{\sqrt{x} ({(\sqrt{x})}^{2} + \sqrt{x} + 1)} + \frac{1}{15} (3 \cos^{5} x - 5 \cos^{3} x) y = (\sqrt{x} + 1) (\sqrt{x} - 1) + \frac{1}{5} \cos^{5} x - \frac{1}{3} \cos^{3} x y^{1} = 1 - \cos^{4} x \sin x + \cos^{2} x \sin x y^{1} (\frac{π}{6}) = \frac{35}{32} \Rightarrow 32 y^{1} (\frac{π}{6}) = 35$