​ (i) Let y =3 cos(log x) + 4 sin (log x) (a) Find (b) Prove that x^2 y_2 + xy_1 + y = 0 ​(ii) (a) Find the derivative of y = e^2x+logx

Question

(i) Let y =3 cos(log x) + 4 sin (log x)

(a) Find \(\frac{dy}{dx}\)

(b) Prove that x² y₂ + xy₁ + y = 0

(ii) (a) Find the derivative of y = e^2x+logx

(b) Find \(\frac{dy}{dx}\)

if x = a (θ – sinθ), y = a(1 – cosθ) 

Answer 1

(i) (a) Given; y  3 cos(logx) + 4 sin(log x)

Differentiating with respect to x;