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, $=2x (-\sin t+\cos t)+2y(-\sin t -\cos t)$
or, $\dfrac{dw}{dt}=2 (\cos t+\sin t) (-\sin t+\cos t)+2 (\cos t- \sin t)(-\sin t -\cos t)=0$
Using direct differentiation.
since, $w^2=x^2+y^2=(\cos t+\sin t)^2+(\cos t -\sin t)^2=2$
and $\dfrac{dw}{dt}=0$
Now, b) $\dfrac{dw}{dt}(0)=0$
