## Study23 Group Title 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!! one year ago one year ago

1. Ventricate Group Title

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 Group Title

Could you explain it to me please?

3. Ventricate Group Title

Are you familiar with the derivative rules?

4. Study23 Group Title

Yes

5. Ventricate Group Title

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 Group Title

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

7. Ventricate Group Title

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

8. Study23 Group Title

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

9. Ventricate Group Title

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

10. Study23 Group Title

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

11. Study23 Group Title

I'm REALLY Confused BY this! !

12. Ventricate Group Title

it's the derivative of y

13. Ventricate Group Title

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

14. Study23 Group Title

Okay