Let z = g(x, y) and suppose that x(t) = t^2 + 3t + 2 and y(t) = e^t + sin(3t) Find (dz/dt)|t=0 if (dg/dx)|(1,2) = 6 (dg/dy)|(1,2) = -2 (dg/dx)|(2,1) = -3 (dg/dy)|(2,1) = 8 (dg/dx)|(0,0) = 0 (dg/dy)|(0,0) = -4 Thank You.
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Originally Posted by DavidWagner Let z = g(x, y) and suppose that x(t) = t^2 + 3t + 2 and y(t) = e^t + sin(3t) Find (dz/dt)|t=0 if (dg/dx)|(1,2) = 6 (dg/dy)|(1,2) = -2 (dg/dx)|(2,1) = -3 (dg/dy)|(2,1) = 8 (dg/dx)|(0,0) = 0 (dg/dy)|(0,0) = -4 Thank You. By the Chain rule we get Now we need to do some calculations and so and so Finally we get
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