Differentiate the following functions:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Differentiate the following functions:

(i)

(ii) -5 tan x + 4 tan x cos x – 3 cot x sec x + 2sec x – 13

Differentiate the following functions:

(i) (2x + 3) (3x – 5)

(ii) x(1 + x)³

(iii)

(iv)

(v)

(vi) (2x² + 5x – 1) (x – 3)

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 .

If , show that .