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If one uses implicit differentiation and get that \[y^'=\frac{ 2x^3-x }{ 2y^3-y }\] Then is the slope of the tangent line at point (x,y) given by just putting the x and y into the equation?

Mathematics
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wait a sec bro?
Absolutely

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Other answers:

  • phi
if you mean x,y have known values, yes, plug them in to find the slope at that point on the curve.
That was what i meant, thank you :)
ghazi, I guess you went to look it up or something so thank you to :)

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