Question

Let w(x,y,z) = x^2+y^2+z^2 where x=sin(8t), y=cos(8t) , z= e^t Calculate dw/dt by first finding dx/dt,...

Let w(x,y,z) = x^2+y^2+z^2 where x=sin(8t), y=cos(8t) , z= e^t

Calculate dw/dt by first finding dx/dt, dy/dt, and dz/dt and using the chain rule

dx/dt =
dy/dt=
dz/dt=

now using the chain rule calculate
dw/dt 0=

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Answer #1

we have

now,

by the chain rules,

......................i)

put t = 0,

....................ii)

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