1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Chain Rule

  1. Sep 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose $$z=x^2 sin(y), x=5t^2-5s^2, y=4st$$
    Use the chain rule to find $$\frac{\partial z}{\partial s} \text{ and } \frac{\partial z}{\partial t}$$

    2. Relevant equations
    $$\frac{\partial z}{\partial s} = \frac{\partial z}{\partial x} \frac{\partial x}{\partial s} + \frac{\partial z}{\partial y} \frac{\partial y}{\partial s}$$

    3. The attempt at a solution
    $$\frac{\partial z}{\partial x} = 2x\sin(y)$$
    $$\frac{\partial x}{\partial s} = -10s$$
    $$\frac{\partial z}{\partial y} = x^2\cos(y)$$
    $$\frac{\partial y}{\partial s} = 4t$$
    With those I then substitute the values into the equation, and I came up with $$\frac{\partial z}{\partial s}=2x\sin(y)(-10s)+x^2\cos(y)(4t)=-20(5t^2-5s^2)(s)\sin(4st)+4(5t^2-5s^2)(t)\cos(4st)$$
    Where am I going wrong? Also, I am still learning Latex, so I apologize for the crude display.
     
  2. jcsd
  3. Sep 12, 2016 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    In the last term you should have ##(5t^2-5s^2)^2##, not ##(5t^2-5s^2)##.
     
  4. Sep 12, 2016 #3
    Thanks! Never fails I overlook something simple like that. Other than that, does it appear that I am going about it correctly?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Chain Rule
  1. Chain rule (Replies: 1)

  2. Chain rule (Replies: 2)

  3. Chain rule (Replies: 22)

  4. Chain rule (Replies: 6)

  5. Chain Rule (Replies: 4)

Loading...