anonymous
  • anonymous
If x^3+y^3−3xy^2=17, find dy/dx in terms of x and y.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Ok so it's been while since I've done this so bear with me.
anonymous
  • anonymous
I believe it is asking you to do the following: What is the derv of x^3? What is the derv of y^3? Whatever you get, you also need to multiply a dy/dx to it as well.
anonymous
  • anonymous
Next is the -3xy^2

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anonymous
  • anonymous
So you have to treat this almost like the product rule. So when we are taking the derivative with respect to x we get, -3y^2 (since the dervative of x=1). Then we need to take the derivative with respect to y. So -3x(2y), since derv of y^2 =2y.
anonymous
  • anonymous
Then the derv of 17 will be 0 since 17 is a constant.
anonymous
  • anonymous
Now we need to combine everything we just learned.
anonymous
  • anonymous
So our equation should look like (keeping in mind that derv of x^3=3x^2, derv of y^3=3y^2dx/dy, derv of -3xy^2 with respect to x is -3y^2, derv of -3xy^2 with respect to y is -3x2y*dy/dx [I forgot to add that in]), we have:
anonymous
  • anonymous
3x^2+3y^2(dx/dy)-3y^2-3x2y*(dy/dx) =0
anonymous
  • anonymous
So now you need to get everything that is not (dy/dx) on the right side and leave dy/dx on the left solve (you're solving for dy/dx)
anonymous
  • anonymous
side*
anonymous
  • anonymous
Does that make sense? I know that is a lot of information to throw at you.

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