Implicit differentiation question?

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Note:   The derivative of eᵁ wrt x is eᵁ(du/dx).

           So, for u=xy,

           d/dx(eˣʸ) = eˣʸ(d/dx(xy)) = eˣʸ(xy'+y*1) = eˣʸ(xy'+y)

                   xy - eˣʸ = 7

(xy'+y*1) - eˣʸ(xy'+y) = 0        ← Differentiated implicitly wrt x ... Now, expand and collect y'-terms

xy' + y - eˣʸxy' - eˣʸy = 0

               xy' - eˣʸxy' = eˣʸy - y

               (x - eˣʸx)y' = (eˣʸ - 1)y

                                     (eˣʸ - 1)y

                            y' = —————–

                                      x - eˣʸx

                                     (eˣʸ - 1)y

                            y' = —————–            ← ANSWER

                                     x(1 - eˣʸ)

Have a good one!

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The derivative of e^x is e^x. Here it's e^xy, so use chain rule for that. Then when solving for dy/dx you'll have to use ln to get rid of the e. Hope that helps