anonymous
  • anonymous
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!!
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • 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?
anonymous
  • anonymous
Could you explain it to me please?
anonymous
  • anonymous
Are you familiar with the derivative rules?

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

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