How Can I Find the Derivatives of this Complex Function Using Derivation Rules?

[efekwulsemmay]

Homework Statement

I am supposed to find the first and second order derivative of
$$p=\left(\frac{q^{2}+3}{12q}\right)\left(\frac{q^{4}-1}{q^{3}}\right)$$

Homework Equations

Derivation Sum and Difference as well as Product and Quotient Rules

The Attempt at a Solution

I tried to cross multiply and use the product rule on the resulting equation but its wrong.
I am not sure what to do.

 

[jgens]

Show us what you've tried so far and then we can help you out.

 

[H2instinct]

Cross multiplication is for when a Fraction = a Fraction. When you multiplied them did you get... (x^2+3)(x^4-1) / 12x^2. Then take the quotient rule of the entire function and don't forget to use the product rule where necessary for the numerator. It'll start to look ugly, but such is calculus sometimes.

I am only a member and I just joined today, but I hope this helps a bit. :|

 

[Luongo]

Ugh. First thing is it's called "differentiation" the process of obtaining the derivative. Derivations are from solving proofs.

 

[lurflurf]

Ugh. First thing is it's called "differentiation" the process of obtaining the derivative. Derivations are from solving proofs.

Differentiation and derivation can both be used. Take for example a derivation algebra. Proofs are not solved they may be found, constructed, studied, verified, or repaired, but not solved.

 

[lurflurf]

One could see this by use of Derivation Sum and Difference as well as Product and Quotient Rules, but expanding the function may be prefered.
[(q^2+3)/(12q)][(q^4-1)/(q^3)]=(q^2+3-q^-2-3q^-4)/12