Let $w(x,y,z)=x^2+y^2+z^2$ where $x=sin(-3t),y=cos(5t),z=e^{-3t}.$

$13$ Calculate $\frac{dw}{dt}$ by first finding $\frac{dx}{dt},\frac{dy}{dt}$&$\frac{dz}{dt}$ and using the chain rule.

$\frac{dx}{dt}=$

$\frac{dy}{dt}=$

$\frac{dz}{dt}=$

Now use the chain rule to calculate the following:

$\frac{dw}{dt}=$

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