Question

Suppose Q=x^1y^4. If dQ/dt=-2 and dx/dt=3, find dy/dt when x=1 and y=1

Answer 1

Implicit differentiation:
\[Q=xy^4~~\Rightarrow~~\frac{dQ}{dt}=y^4\frac{dx}{dt}+4xy^3\frac{dy}{dt}\]
Plug in the given info.

Answer 2

i am getting -2/7. It is coming out wrong?

Answer 3

I am putting -2=(1)^4 times 3+4(1)(1)^3dy/dt

Answer 4

Maybe I am putting it in the calculator wrong

Answer 5

\[-2=(1)^4(3)+4(1)(1)^3\frac{dy}{dt}~~\Rightarrow~~-2=3+4\frac{dy}{dt}~~\Rightarrow~~\frac{dy}{dt}=-\frac{5}{4}\]

Answer 6

Got it. Thanks

Answer 7

yw