Solving Derivative dy/dx: y, sin(xy) + 1 = cos x

  • Thread starter Thread starter skyhawk714
  • Start date Start date
  • Tags Tags
    Derivatives
skyhawk714
Messages
4
Reaction score
0
1. Find the derivatie of y, dy when e/\(y) cos x=1 + sin (xy)
---
dx

2. I don't know of any Relevant equations


3. The first time i tried the problem i got e/\(y) cos X+ y cos (xy)
------------------------
e/\(y) sin x- x cos (xy)

but i know that's not right...how do i even do a problem like this?
 
Physics news on Phys.org
You are trying to use implicit differentiation to find dy/dx given (e^y)*cos(x)=1+sin(xy), right? Your answer has the right sort of general form, but it's not correct. Differentiate both sides of (e^y)*cos(x)=1+sin(xy) using the chain rule and show the steps you did to get your answer.
 
Last edited:
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