## anonymous 5 years ago differentiate: xy=[(x+3y)^4]+7

1. anonymous

dy / dx or dx / dy ?

2. anonymous

The total differential is: $y \text{Dt}[x]+x \text{Dt}[y]=4 (x+3 y)^3 (\text{Dt}[x]+3 \text{Dt}[y])$

3. 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] $\frac{\text{Dt}[y]}{\text{Dt}[x]}=\frac{\left(4 x^3-y+36 x^2 y+108 x y^2+108 y^3\right) }{x-12 (x+3 y)^3}$

4. anonymous

Thankyou for the medal, cara.

5. 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!

6. anonymous