Answer
a) $-\frac{1}{4}$
b) $-16$
Work Step by Step
$x+4y=3$
Taking derivative with respect to t
$\frac{d(x+4y)}{dt}= \frac{d(3)}{dt}$
$\frac{dx}{dt}+\frac{d(4y)}{dt}=0$
$\frac{dx}{dt}+4\frac{dy}{dt}=0$ ....................... eq (1)
(a) Putting $\frac{dx}{dt}=1$ i equation (1)
$1+4\frac{dy}{dt} =0$ Or
$4\frac{dy}{dt}=-1$ Or
$\frac{dy}{dt}=-\frac{1}{4}$
(b)Putting $\frac{dy}{dt}=4$ in equation (1)
$\frac{dx}{dt}+4\times 4=0$
$\frac{dx}{dt}=-16$
