InterviewSolution
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InterviewSolution
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Differentiate the following w.r.t.x and find the value when x =9. (i) sin 5x (ii) tan 5x (iii) cos 5x |
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Answer» Correct Answer - (i) `5//sqrt2` (ii) 10 (iii) `-5 // sqrt2` (i) Let `u =5x, (du)/(dx) = 5 so, y =sin u and (dy)/(du) = cos u = cos 5 x` `:. (dy)/(dx) =(dy)/(du)xx(du)/(dx) = cos 5x xx5 = 5 cos 5x when x =9, (dy)/(dx) = 5cos 5xx9 = 5 cos 45^@ =5xx(1)/(sqrt2)` (ii) `(dy)/(dx) = (d)/(dx)(tan 5x) = sec^25x xx(d)/(dx)(5x) = sec^25x xx5` when `x =9, (dy)/(dx) = 5 sec^2 5xx9 = 5xx(sqrt2)^2 =10` (iii) `(dy)/(dx) = (d)/(dx)(cos 5 x) = - 5 sin 5x = - 5 sin 5xx9 = -(5)/(sqrt2)` |
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