Derivative Problem: Step-by-Step Solution

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The Attempt at a Solution



I took the derivative first and got dy/dx = 2 - 1/x. I then substituted and got the answer 1. I'm confused if I was supposed to use dy/dt at all during this problem, and I don't know if I took the right steps.
 
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brambleberry said:

The Attempt at a Solution



I took the derivative first and got dy/dx = 2 - 1/x. I then substituted and got the answer 1. I'm confused if I was supposed to use dy/dt at all during this problem, and I don't know if I took the right steps.


So, what's your question?
 
brambleberry said:

The Attempt at a Solution



I took the derivative first and got dy/dx = 2 - 1/x. I then substituted and got the answer 1. I'm confused if I was supposed to use dy/dt at all during this problem, and I don't know if I took the right steps.
Please tell us what the problem is! What did you differentiate to get dy/dx? This makes no sense at all.
 
brambleberry said:

The Attempt at a Solution



I took the derivative first and got dy/dx = 2 - 1/x. I then substituted and got the answer 1. I'm confused if I was supposed to use dy/dt at all during this problem, and I don't know if I took the right steps.

i suppose this should be differentiate with respect to x if not there would still be variables of t in your equation of first derivative.
 
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...
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