InterviewSolution
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InterviewSolution
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Let `z=(cosx)hat5a n dy="sin"xdot`Then the value of `2(d^2z)/(dy^2)a tx=(2pi)/9`is____________. |
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Answer» `z=(cos x)^(5),y=sin x` `(dz)/(dx)=-5cos^(4)xcdot sin x, (dy)/(dx)= cos x` `therefore" "(dz)/(dy)=-5cos^(3)x cdot sin x` `"Now, "(d^(2)z)/(dy^(2))=(d)/(dx)((dz)/(dy))cdot(dx)/(dy)` `=-5(d)/(dx)[cos^(3)xcdot sin x] (1)/(cos x)` `=-5[cos^(4)x- 3 sin^(2)xcdot cos^(2)x ](1)/(cos x)` `=-5(cos^(3)x-3 sin^(2)xcdotcos x)` `=-5(cos^(3)x-3 cos x(1-cos^(2)x))` `=-5(4 cos^(3)x-3 cos x)` `=-5 cos 3x` `therefore" "(d^(2)z)/(dy^(2)):|_(x=(2pi)/(9))=-5 cos 120^(@)=(5)/(2)` |
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