Differentiate each of the following functions with respect to𝑥:

(i) 𝑓(𝑥) = 3𝑥 5 − 2𝑥 −4 − 5𝑥 3 + 𝑥 −1

(ii) 𝑔(𝑥) = √𝑥 4 3 − 5√𝑥 + 4𝜋

(iii) ℎ(𝑥) = 5𝜋 tan 3𝑥 − 4 cos 5𝑥 (3 marks)

Using an appropriate rule in each case, differentiate thefollowing functions with respect to 𝑥:

(i) 𝑓(𝑥) = 5(𝑥 3 − 2𝑥) 3

(ii) 𝑔(𝑥) = 4 𝑐𝑜𝑠4 (3𝑥 + 1)

(iii) ℎ(𝑥) = (3𝑥 3 − 1)ln (3𝑥 + 2)

(iv) 𝑘(𝑥) = 𝑒 2𝑥+5 𝑒 𝑥+3