Let w = z - sinxy, and suppose that (x(t),y(t),z(t)) = (t,lnt,e^t-1). Use the chain rule to find dw/dt when t = 1.I have a math problem for my calculus III class that i cant figure out?
dw/dt = dz/dt - cos(xy) * (x * dy/dt + y * dx/dt)
(x,y,z) = (1,0,1)
dx/dt = 1
dy/dt = 1/t
dz/dt = e^(t-1)
eval all at t=1
(1,1,1)
dw/dt = dz/dt - cos(xy) * (x * dy/dt + y * dx/dt)
dw/dt = 1 - cos(0) * (1 * 1 + 0 * 1)
= 1 - (1) (1 + 0)
= 1 - 1 = 0
dw/dt = 0
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