Question

Determine the slope of the graph of x^2 = ln(xy) at the point (1, e).

Answer 1

Given: x^2 = ln(xy)

The solution for this problem is:

e^x^2 = xy

y = (e^x^2)/x;

f(x) = (e^x^2);

f'(x) = 2x*(e^x^2);

g(x) = x; g'(x) = 1

[2(x^2)(e^x^2) - (e^x^2)]/x^2 = (e^x^2)(2*(x^2) - 1)/x^2;

plug in x = 1 then this will give us the slope, correct answer which is e.