How do u implicitly differentiate (xy)^1/2

  • Thread starter Thread starter engineer_dave
  • Start date Start date
  • Tags Tags
    Differentiate
engineer_dave
Messages
35
Reaction score
0

Homework Statement



How do u implicitly differentiate (xy)^1/2

Homework Equations





The Attempt at a Solution



Would it be 1/2(xy)^-1/2 multiplied by 1 and dy/dx. Thanks
 
Physics news on Phys.org
It looks like you are trying to use the chain rule so you are on the right track. What's d/dx of xy? BTW, so far, this isn't implicit differentiation.
 
what do u mean it isn't implicit differentiation?
 
It's just differentiation. Implicit differentiation is where you take d/dx of an equation and then solve for dy/dx. There's no equation yet. And you haven't answered my question.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top