If x^3+y^3−3xy^2=17, find dy/dx in terms of x and y.
Stacey Warren - Expert brainly.com
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Ok so it's been while since I've done this so bear with me.
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.
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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.
Then the derv of 17 will be 0 since 17 is a constant.
Now we need to combine everything we just learned.
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:
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)
Does that make sense? I know that is a lot of information to throw at you.