Implicit Differentiation? Don't Understand it :( PLEASE HELP! Here's the problem I am looking at: $\ \large x^3+x^2y+4x^2=6 .$
Find $\ \frac{dy}{dx}. $ Please show me STEP by STEP!!

Question

Implicit Differentiation? Don't Understand it :( PLEASE HELP! Here's the problem I am looking at: $\ \large x^3+x^2y+4x^2=6 .$ 
Find $\ \frac{dy}{dx}. $ Please show me STEP by STEP!!

anonymous · Answer

3x^2+2xy+2x dy/dx +8x= 0 then isolate dy/dx and simplify from there. Do you get that or need me to explain it?

anonymous · Answer

Could you explain it to me please?

anonymous · Answer

Are you familiar with the derivative rules?

anonymous · Answer

Yes

anonymous · Answer

Ok so the first part 3x^2 is from the normal derivative way and then when we move on to derive x^2y we have to use the product rule : (x^2)(y) The product rule I hope you know already is (a'(x)*b)+(a*b'(x)) for ab respectively. Do you understand up to here?

anonymous · Answer

How does the product rule look like when you derive $\ x^2y?$

anonymous · Answer

It should be f'(x) *y + f(x) *y'. Derivative of x^2 is 2x and derivative of y is dy/dx.

anonymous · Answer

Could you show me the product rule in terms of $\ x^2y \text{, please?}$

anonymous · Answer

Sure (2x)(y) +(x^2)(dy/dx)

anonymous · Answer

What does the dy/dx mean? dy/dx of x^2? or y?

anonymous · Answer

I'm REALLY Confused BY this! !

anonymous · Answer

it's the derivative of y

anonymous · Answer

Let's say you had y^3 you would derive it as $$3y^2 \frac{ dy }{ dx }$$

anonymous · Answer

Okay