## anonymous 4 years ago 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!!

1. anonymous

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?

2. anonymous

Could you explain it to me please?

3. anonymous

Are you familiar with the derivative rules?

4. anonymous

Yes

5. anonymous

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?

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

I'm REALLY Confused BY this! !

12. anonymous

it's the derivative of y

13. anonymous

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

14. anonymous

Okay