Consider the following Function: W = y^3 - 4x^2 y, x = e^s, y = e^t Point: s = 0

Question

Consider the following Function: W = y^3 - 4x^2 y, x = e^s, y = e^t Point: s = 0, t = 3 Find partial differential s and partial differential w/partial differential t using the appropriate Chain Rule. partial differential w/partial differential s = partial differential w/partial differential t = Evaluate each partial derivative when s = 0 and t = 3. (Give your answer correct to the nearest whole number.) partial differential w/partial differential s = partial differential w/partial differential t =

Explanation / Answer

Solution:

As alredy solved

dw/ds = -8e^(2s + t) and dw/dt = 3e^(3t) - 4e^(2s) e^(t)

So value of partial derivative at s = 0 and t = 3;

dw/ds = -8e^(2*0 + 3) = -8e^3 = -8*(20.08) = - 160.64 = -161

And

dw/dt = 3e^(3*3) - 4e^(2*0) e^(3) = 3e^9 - 4e^(0) e^(3) = 3e^9 - 4e^3 = 24309.25 - 80.34 = 24228.91 = 24229

So

dw/ds = -161

dw/dt = 24229

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