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