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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