Question

Determine the slope of the graph of x3 = ln(xy) at the point (1, e).

Answer 1

I am thinking one or three.

Answer 2

have you learned implicit differentiation or anything or that sort?

Answer 3

yes that is what this is

Answer 4

You can isolate y.

\[x^3 = \ln(xy)\\~\\\ln y = x^3 - \ln x\\~\\y = e^{x^3-\ln x}\\~\\y = e^{x^3}e^{-\ln x} \\~\\y = \dfrac{e^{x^3}}{x}\]

You can take derivative of y, then plug in 1 to get a answer.

Answer 5

So 3 would be the answer?

Answer 6

\(3\)?

I got \(2e\)

Do you understand what I did to isolate y?

What do you get after taking derivative of y?