Differentiate the following functions with respect to x :
(i) `x^(3)+2x^(2)+1 " "` (ii) `e^((3x+2)) " "` (iii) `cos^(2) x`

Explanation

(i)`(d)/(dx)(x^(3)+2x^(2)+1)`
`=(d)/(dx)(x^(3))+ (2d(x^(2)))/(dx)+(d(1))/(dx)`
`=3x^(2)+4x`
(ii)`(d)/(dx)e^((3x+2))=(d(e^(3x+2)))/(d(3x+2))(d(3x+2))/(dx)`
`=3e^((3x+2))`
(iii) `y=cos^(2)x`
`(dy)/(dx)=(d(cos^(2)x))/(d(cos x)).(d(cos x))/(dx)`
`=-2 cos x sin x `
`=-sin 2 x`