Differentiate the following functions with respect to xuse

Question

1. Differentiate the following functions with respect to x.

(a) Use the quotient rule to differentiate

y= 2x⁴ - 3x/4x - 1

(b) Use the Chain rule to differentiate

y = 6cos(x³ + 3)

(c) Select an appropriate rule to differentiate

y = (4x² - e^2x )sin3x

2. Find the following integrals,

(a) ∫(5x²+√x-4/x²)dx

(b) ∫[cos(x/2)-sin(3x/2]dx

(c) ₁⁵∫s/√s²+4ds

3. (a) Find the area bounded by the curve y = 1/x between x =2 and x =6. (Give your answer to 3 decimal places.)

(b) Sketch the curve for y = sin(x) between x =0 and x =2Π then find the total area enclosed by the curve y = sin x and the X axis between x=0 and x= 1.7Π