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How do you use implicit differentiation to find a basis for the tangent plane?

nyvan

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12 years ago

How do you use implicit differentiation to find a basis for the tangent plane?

If we have the function f(x,y,z) = (xyz)^(1/3)
How do we apply implicit differentiation to find a basis for the tangent plane through (1,1,1)?

I am a little unsure of how to apply this differentiation when it involves a function of three variables.
Any help would be very much appreciated! Thank you!

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