How to find the derivative of g(x) = 6x^2 / 2-x

Question

3psilon · Answer

My teacher says you don't need the quotient rule to do it

anonymous · Answer

Using the product and chain rules, this is rather simple:
We know:
$$
g'(x)=\frac{d}{dx}(6x^2)(2-x)^{-1}=(12x)(2-x)^{-1}+6x^2\left(\frac{d}{dx}(2-x)^{-1}\right)
$$
From this, you should be able to get it.

campbell_st · Answer

ok... so your teacher uses the product rule... rewrite the problem as 

$$y = 6x^2 \times (2 -x)^{-1}$$

and work from there

3psilon · Answer

Ahhhh I knew there was a way to write it in product form . Just forgot . Thanks

3psilon · Answer

@LolWolf would 
d/dx  of $$(2-x)^{-1}$$ just be -1? Sorry I'm new to derivatives

anonymous · Answer

Remember that we can us the chain rule to specify that $$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$$So, we apply this to show:$$\frac{d}{dx}(2-x)^{-1}=-1(2-x)^{-2}(-1)=(2-x)^{-2}$$And we are done.

anonymous · Answer

And, it's all right, if you need any further help, PM me.