anonymous
  • anonymous
let z=f(x,y)=x/y, x=p+q,y=p-q. find fp (f sub p)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
fp has 2 components; fx and fy; such that xp and yp are the resulting paths
amistre64
  • amistre64
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amistre64
  • amistre64
|dw:1333216039644:dw|

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amistre64
  • amistre64
f x + f y x p y p is the general set up from the chain rule for partials
TuringTest
  • TuringTest
can we not just do\[f=\frac xy=\frac{p+q}{p-q}\]and then take the partial with respect to p ?
amistre64
  • amistre64
you can, but at times that can get complicated and its useful to be able to apply the chain rule for things. I beleive this example was just a primer to build confidence tho
anonymous
  • anonymous
how do you use the chain rule for this? my teacher never really taught us!
amistre64
  • amistre64
its the same concept as when you first learnt it back in calc1 f(g(x)) derives to f'(g(x))* g'(x)
amistre64
  • amistre64
in this case; lets hold x and q constant and go for y \[f(y(p))\to f_y*y_p\] and if we hold y and q constant \[f(x(p))\to f_x*x_p\] together each part defines \(f_p\)
amistre64
  • amistre64
\[f_p=f_xx_p+f_yy_p\]
anonymous
  • anonymous
thank you so much!

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