anonymous
  • anonymous
differentiate: xy=[(x+3y)^4]+7
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
dy / dx or dx / dy ?
anonymous
  • anonymous
The total differential is: \[y \text{Dt}[x]+x \text{Dt}[y]=4 (x+3 y)^3 (\text{Dt}[x]+3 \text{Dt}[y]) \]
anonymous
  • anonymous
For dy/dx solve the equation for Dt[x] \[\text{Dt}[y]=\frac{-y \text{Dt}[x]+4 (x+3 y)^3 \text{Dt}[x]}{x-12 (x+3 y)^3} \] Factor the right side for Dt[x] \[\text{Dt}[y]=\frac{\left(\left(4 x^3-y+36 x^2 y+108 x y^2+108 y^3\right) \text{Dt}[x]\right)}{x-12 (x+3 y)^3} \] Divide each side by Dt[x] \[\frac{\text{Dt}[y]}{\text{Dt}[x]}=\frac{\left(4 x^3-y+36 x^2 y+108 x y^2+108 y^3\right) }{x-12 (x+3 y)^3} \]

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anonymous
  • anonymous
Thankyou for the medal, cara.
anonymous
  • anonymous
no problem thanks for ur help!! u do it a bit differently than my teacher so i was a bit confused at first but i figured it out lol thanks!
anonymous
  • anonymous
Your welcome.
anonymous
  • anonymous
As an aside, "For dy/dx solve the equation for Dt[x]" should have been typed: "For dy/dx solve the equation for Dt[y]" Very Sorry.

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