Question

Using the chain rule and implicit differentiation, determine

Answer 1

Determine \[\frac{ du }{ dt }\] where u(x; y) = x3y and \[\left\{ x ^{5}+y=t \right\}\] \[\left\{ x^2+y^3=t ^{2} \right\}\]

Answer 2

where u(x; y) = x^3 y and

Answer 3

@zepdrix pls help

Answer 4

Hmm this looks a little confusing.. lemme see if I've got this straight.

u is a function of x and y,
x and y are functions of t?

So the derivative of u with respect to t gives us ( by the chain rule ):\[\Large\rm =\frac{\partial u}{\partial x}\cdot\frac{dx}{dt}+\frac{\partial u}{\partial y}\cdot\frac{dy}{dt}\]

So we need to calculate some derivatives, yes? :o

Answer 5

Or y is a function of x and t?
Hmm weird problem :O

Answer 6

yo chain rule expression looks ok