solve for dv/du

Question

dQ/du= 38u + [(u+v)^2(18+19dv/du) -(2(18u+19v)(u+v)(1+dv/du)]/ (u+v)^4

u=10 v=25

I am confused how u solve for the dv/du in this big equation and reducing and stuff like that

thanks!! this is about implicit di

Answer 1

looking at the pattern of your answer, it looks like there were 2 terms and the quotient rule was used on the second term

looks like you had

Q = 19u^2 + (18u+19v(/(u+v)^2
and you took the derivative with respect to u

since you know the value of u and v, you can shave down that messy looking right side quite a bit

dQ/du = 380 + [ 35^2(18 + 19dv/du) - 2(655)(25)(1+dv/du) ] 35^4
If you were somehow finding max/min, then dQ/du would be zero, otherwise I don't know what value the left side is
But you have a calculator, just crunch out the numbers. You will have to distribute 35^(18+19dv/du) and the second part of the numerator to get at the dv/du, but hang in there.
Eventually you will be able to collect the dv/du terms, since the other parts are constants.