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# Using chain rule find $\large\frac{dw}{dt}$ for each of the following$\;w=xy+z$ where $x=\cos t,y=\sin t$

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• Chain rule: If $u= f(x,y)$ is differentiable and $x,y$ are functions of t then $\large\frac{du}{dt}=\frac{\partial u}{\partial x}\frac{dx}{dt}+\frac{\partial u}{\partial y} \frac{dy}{dt}$
• The chain rule for $u(x,y,z)$ where $x,y,z$ are functions of t is similarly stated.
$w=xy+z\;x=\cos t,\;y=\sin t\;z=t$
$\large\frac{dx}{dt}$$=-\sin t,\large\frac{dy}{dt}$$=\cos t,$$\large\frac{dz}{dt}=$$1$