What is the slope of eln(2x^4+ax^2y^2+2y^4) ?

The slope of eln(2x^4+ax^2y^2+2y^4) is (8ex^3+2eaxy^2)/(2x^4+ax^2y^2+2y^4-2eax^2y-8ey^3)

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slope of eln(2x^4+ax^2y^2+2y^4)

slope

e ln (2 x^{4} + a x^{2} y^{2} + 2 y^{4})

\frac{8 e x ^{3} + 2 e a x y ^{2}}{2 x ^{4} + a x ^{2} y ^{2} + 2 y ^{4} - 2 e a x ^{2} y - 8 e y ^{3}}

Solution steps

y = e ln (2 x^{4} + a x^{2} y^{2} + 2 y^{4})

Use implicit differentiation to find the slope of

y = e ln (2 x^{4} + a x^{2} y^{2} + 2 y^{4})

Implicit Derivative

\frac{d y}{d x}

y = e ln (2 x^{4} + a x^{2} y^{2} + 2 y^{4}) : \frac{8 e x ^{3} + 2 e a x y ^{2}}{2 x ^{4} + a x ^{2} y ^{2} + 2 y ^{4} - 2 e a x ^{2} y - 8 e y ^{3}}

\frac{8 e x ^{3} + 2 e a x y ^{2}}{2 x ^{4} + a x ^{2} y ^{2} + 2 y ^{4} - 2 e a x ^{2} y - 8 e y ^{3}}

What is the slope of eln(2x^4+ax^2y^2+2y^4) ?
The slope of eln(2x^4+ax^2y^2+2y^4) is (8ex^3+2eaxy^2)/(2x^4+ax^2y^2+2y^4-2eax^2y-8ey^3)