f(t)=(3t-1)^4*(2t+1)^6

In expanded form:

f(t) = 5184 t^10+8640 t^9+2160 t^8-3360 t^7-1700 t^6+444 t^5+345 t^4-20 t^3-30 t^2+1

In awnser to your second question;

Chan rule is essentially used to differentiate anything in silly brackets - ie. if the powers of the brackets mean that binomial expansion would take too long. ie.\({(x^2+x+1)}^{5}\)

 

The product rule is used to differentiate any chain rule (ie. any silly bracket powers) when they are multiplied by anything esle; ie \(x{(x^2+x+1)}^{5}\)

 

The quotient rule is used when you have a chain rule, but it is part of a fraction. ie\(\frac{x}{{(x^2+x+1)}^{5}}\)

However - the quotient rule is simply the product rule in a different form - i would reccomend turning all quotient rule questions into product rule questions; as \(\frac{x}{{(x^2+x+1)}^{5}}\)\(= (x){(x^2+x+1)}^{-5}\)