How to find the derivative of xy = in (x² + y ² )? show all workings and simplify! the answer is supposed to be yx^2+y^3 -2x / 2y - x^3-xy^2

Step-by-step explanation:

Keep in mind that the derivative of ln(u) = u'/u.  Here, our u is x^2 + y^2, so the derivative of that will fit in for u'.  Let's do this step by step:

Working on the left first, using the product rule, the derivative (implicite, of course!) is:

Now we will work on the right side, keeping in mind the rule above for derivatives of natural logs:

Now we are going to get rid of the donominator on the right by multiplication on both sides:

Distribute on the left to get

Now collect all the terms with dy/dx in them on one side and everything else goes on the other side:

Factor out the common dy/dx:

and divide on the left to isolate the dy/dx:

And there you go!

answer: i literally just answered this question but they want me to do it again

step-by-step explanation:

the answer for your question is

step-by-step explanation: