Hello everybody, I am having some trouble with how to approach this question:
Problem #6: Suppose that f is a differentiable function, with fx (0, 0) = 3 and fy (0, 0) = 7. Let w(u, v) = f (x (u, v), y (u, v)), where x = 5 cos(u) + 3 sin(v) and y = 6 cos(u) sin(v).
Find \(\displaystyle \, w_v\left(\dfrac{\pi}{2},\, 0\right)\)
I understand I have to apply the chain rule but the fact that the x and y points are multivariable functions themselves is cluttering my thought process. Any insight would be great.
Problem #6: Suppose that f is a differentiable function, with fx (0, 0) = 3 and fy (0, 0) = 7. Let w(u, v) = f (x (u, v), y (u, v)), where x = 5 cos(u) + 3 sin(v) and y = 6 cos(u) sin(v).
Find \(\displaystyle \, w_v\left(\dfrac{\pi}{2},\, 0\right)\)
I understand I have to apply the chain rule but the fact that the x and y points are multivariable functions themselves is cluttering my thought process. Any insight would be great.
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