(a) Given that

\(y=\frac{1+\cos^2x}{\tan x},\)

use differentiation to find the approximate change in \(y\) as \(x\) increases from \(\frac{\pi}{4}\) to \(\frac{\pi}{4}+h\), where \(h\) is small.

(b) Given that

\(y=\frac{1}{(x-3)^3},\)

show that

\(y-\frac{dy}{dx}-\frac13\frac{d^2y}{dx^2}\)

can be written as

\(\frac{(x+1)(x-4)}{(x-3)^5}.\)