Differentiate the following with respect to x.
(i) `sin 2x` (ii) `cos 3x` (iii)` tan 4x` (iv) `sin^3x` (v) `x^2//tan x`

Options

A. `2 cos 2x`, `- 3 sin 3x`
B. `2 cos 2x` , ` 3 sin 3x`
C. `2 cos 2x ,` `- 4 sin 3x`
D. `2 cos 2x`, ` 3 sinx`

Answer

A

Explanation

(i) `y = sin 2x , (dy)/(dx) = cos 2x (d)/(dx) (2x) = (cos 2x)xx2 =2 cos 2x`
(ii)` y =cos 3x , (dy)/(dx) , = - sin 3x (d)/(dx) (3x) =- 3 sin 3x`
(iii) `y = tan 4x , (dy)/(dx) =sec^2 4x (d)/(dx) (4x) = 4sec^2 4x`
(iv) ` y =sin^3 x, (dy)/(dx) = (d)/(dx) (sin x)^3 =3 (sin x)^2 (d)/(dx) (sin x) = 3 sin^(2) x cos x`
(v) `y = x^(2)// tan x = x^(2) cot x`
`(dy)/(dx) = x^(2) (d)/(dx) (cot x) + cot x(d)/(dx) (x^(2)) = x^(2) (- cosec^2 x) +cot x(2x) =- x^(2) cosec^(2) x +2x cot x`