## Study23 2 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. Ventricate

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. Study23

Could you explain it to me please?

3. Ventricate

Are you familiar with the derivative rules?

4. Study23

Yes

5. Ventricate

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. Study23

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

7. Ventricate

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

8. Study23

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

9. Ventricate

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

10. Study23

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

11. Study23

I'm REALLY Confused BY this! !

12. Ventricate

it's the derivative of y

13. Ventricate

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

14. Study23

Okay