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Use implicit differentiation to find the slope of the tangent line to the curve defined by xy6+6xy=42xy6+6xy=42 at the point (6,1)(6,1).

the slope of the tangent line to the curve at the given point is

Respuesta :

The given curve is xy⁶ + 6xy = 42.

Perform the implicit differentiation.
y⁶ + 6xy⁵y' + 6y + 6xy' = 0
y'(6xy⁵ + 6x) + y⁶ + 6y = 0
[tex]y'=- \frac{y^{6}+6y}{6xy^{5}+6x } [/tex]

At the point (6,1), the slope is
[tex]y'(6,1)=- \frac{1+6}{6(6)+6(6)}=- \frac{7}{72} [/tex]

Answer: [tex]- \frac{7}{72} [/tex]

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