Answer
a. $0$ b. $0$
Work Step by Step
a. Using chain rule:
$\dfrac{dw}{dt}=\dfrac{\partial w}{\partial x}\dfrac{dx}{dt}+\dfrac{\partial w}{\partial y}\dfrac{dy}{dt}=-2x \sin t+2y \cos t$
and, $-2\cos t \sin t+2 \sin t \cos t=0$
b. Using direct differentiation:
we have $w^2=x^2+y^2=\cos^2 t+\sin^2 t=1$
and $\dfrac{dw}{dt}=0$
Then, $\dfrac{dw}{dt}(\pi)=0$
