Find dz using the chain rule. Assume the variables are restricted to dt domains on which the functions are defined. z = ay , x = e , y = sint NOTE: Enter your answer as a function of t only. dz 2 e-2t sin (t) + e-2 cos(t) X dtdz Given that z = x sing + y sinx, x = t and y = Int, find using the dt chain rule. Assume the variables are restricted to the domain on which the functions are defined. NOTE: Enter the exact answer as a function of t. dz dtGiven that z = In (a28 + y28), x = - and y = vt, find dz dt using the chain rule. Assume the variables are restricted to the domain on which the functions are defined. NOTE: Enter the exact answer as a function of t. dz dtdz Given that z = (x ty)ey, x = 18t and y = 1 -tl8, find using the dt chain rule. Assume the variables are restricted to the domain on which the functions are defined. NOTE: Enter the exact answer as a function of t. dz = dtGiven that z = sin (@ 18 , x = Inu and y = v, find and av Assume the variables are restricted to the domain on which the functions are defined. NOTE: Enter exact answers as a functions of u and v only. Oz Oz avOz Given that z = xey, x = ul + v and y = ul5 - v], find and av Assume the variables are restricted to the domain on which the functions are defined. NOTE: Enter exact answers as a functions of u and v only. Oz Oz av