anonymous
  • anonymous
Use the chain rule to find ∂f/∂s and ∂f/∂t for a di erentiable function f(x, y) where x(s; t) = s^2- t^2 ; y(s, t) = st:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
http://www.math.hmc.edu/calculus/tutorials/multichainrule/
anonymous
  • anonymous
Thank you for your kind assistance
zepdrix
  • zepdrix
So we have some function \(\large f(x,y) \qquad = \qquad f\left(x(s,t),y(s,t)\right)\) Taking the partial derivative with respect to s gives us,\[\large \frac{\partial f}{\partial s} \qquad = \qquad \color{royalblue}{\frac{\partial f}{\partial x}}\cdot \frac{dx}{ds}+\color{royalblue}{\frac{\partial f}{\partial y}}\cdot\frac{dy}{ds}\] Hmmm, they didn't tell us what \(\large f\) is. So I don't think you can do anything with those blue terms.

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zepdrix
  • zepdrix
Oh our x and y are written in terms of 2 variables, i should have probably wrote partials for those chain rules :( Ugh my bad...

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