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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!!
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?
Could you explain it to me please?
Are you familiar with the derivative rules?
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?
How does the product rule look like when you derive \(\ x^2y?\)
It should be f'(x) *y + f(x) *y'. Derivative of x^2 is 2x and derivative of y is dy/dx.
Could you show me the product rule in terms of \(\ x^2y \text{, please?}\)
Sure (2x)(y) +(x^2)(dy/dx)
What does the dy/dx mean? dy/dx of x^2? or y?
I'm REALLY Confused BY this! !
it's the derivative of y
Let's say you had y^3 you would derive it as \[3y^2 \frac{ dy }{ dx }\]