Find and simplify the derivative (quotient rule)

[anonymity]

Homework Statement

find the derivative of (x² - 3)⁴/(2x³+1)³

and simplify

Homework Equations

The Attempt at a Solution

as far as i could get was 8x(x²-3)³-18x²(2x³+1)²/(2x³+1)⁶

which is not simplified.

How can you simplify something like this? Is there a systematic way to approach it?

In general, what is the best method to approach really messy derivatives (such as this one, or any other that can be manipulated by algebra)?

 

[hunt_mat]

Check your calculation: $$u=(x^{2}-3)^{4}$$ and $$v=(2x^{3}+1)^{3}$$, then:
$$\frac{du}{dx}=8x(x^{2}-3)^{3}\quad\frac{dv}{dx}=18x^{2}(2x^{3}+1)^{2}$$
From here the algebra is doable.

 

[anonymity]

Doh. Thanks lol