Differentiate the following functions:

(i) If y = 6x⁵ – 4x⁴ – 2x² + 5x – 9, find at x = -1.

(ii) If y = (sin x + tan x), find at .

(iii) If , find at .

Formulae:

= n

- cosec²x

- cosecx cotx

sec²x

cosx

(i) If y = 6x⁵ – 4x⁴ – 2x² + 5x – 9, find at x = -1.

Differentiating with respect to x,

6x⁵ - 4x⁴ – 2x² + 5x – 9

30x⁴ -16x³ – 4x + 5

(_{x = -1} = 30(-1)⁴ -16(-1)³ – 4(-1) + 5

= 30+16+4+5

= 55

(ii) If y = (sin x + tan x), find at .

Differentiating with respect to x,

sinx + tanx) = cos x + sec² x

Substituting

_{x = π/3} = cos + sec²

= + 4

=

(iii) If , find at .

Differentiating with respect to x,

2cosec x-3cot x) = 2(- cosecx cotx) – 3(- cosec²x)

Substituting

_{x = π/4} = 2(- cosec cot) – 3(- cosec²)

= - 2× + 3×2

= 6 - 2×