Question 2: (10 pts) Find the total differential of the function a) f(x, y) = ye^x at (0, 3) b) f(x, y) = sqrt(x^2 + y^3) at the point (3, 1)
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Given that \(f(x,y) = ye^x\), we have \(f_x = ye^x\) and \(f_y = e^x\). At point P, we have \(f(0,3) = 3e^0 = 3\). Therefore, the total differential is \(df = f_x \cdot dx + f_y \cdot dy = 3dx + dy\). ** Show more…
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