Differentiate the following w.r.t.x and find the value when x =9.
(i) `sin 5x" "(ii) tan 5x" "(iii) cos 5x`

Options

A. (i) `5//sqrt3` (ii) `5` (iii) `-5 // sqrt3`
B. (i) `25//sqrt2` (ii) `5` (iii) `-5 // sqrt2`
C. (i) `5//sqrt2` (ii) `10` (iii) `-5 // sqrt2`
D. (i) `5//sqrt2` (ii) `10` (iii) `-7 // sqrt3`

Answer

C

Explanation

(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)`