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Verified Answer :

nobillionaireNobley

∂z/∂s = dz/dx dx/ds + dz/dy dy/ds
dz/dx = 2x sin(y)
dx/ds = 4s
dz/dy = x^2 cos(y)
dy/ds = 4t

∂z/∂s = 2x sin y 4s + x^2 cos y 4t = 8sx sin(y) + 4tx^2 cos(y)

∂z/∂t = dz/dx dx/dt + dz/dy dy/dt
dz/dx = 2x sin(y)
dx/dt = -8t
dz/dy = x^2 cos(y)
dy/dt = 4s

 ∂z/∂t = 2x sin y -8t + x^2 cos y 4s = -16tx sin(y) + 4sx^2 cos(y)

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