I need help doing a Midterm Practice Question.
Attempt: I tried finding each individual partial derivative and adding them together initially. I ended up getting something extremely complicated for x, y and z and they didn't end up amounting to 0. For x it was: -x(-3/2)(x^2 + y^2 + z^2)^(-5/2)(2x) -x(x^2 + y^2 + z^2)^(-3/2) == 6x^2(x^2 + y^2 + z^2)^(-5/2) - x(x^2 + y^2 + z^2)^(-3/2)
Any help you could give would be great. Thank you so much in advance!
Your basic approach is correct: to solve the problem, you have to compute the partial derivatives, and it looks like you have a good handle on how to do that. If your answer isn't coming out right, you made a mistake somewhere in your calculations. Look over them carefully, and you should be able to find the error.