Question

find the equation of the horizontal tangent line(s) of y=(x^2)^x

Answer 1

so horizontal tangent line will have a slope of 0, which makes the derivative 0...I need to find dy/dx, i'm guessing

I don't know where to start

Answer 2

take ln both sides to get exponent of x down
the left hand side will by lny , It becomes lny = x ln x^2 =2xlnx
take derivative both sides, you have y'/y = .....
isolate y' and let it =0

Answer 3

don't forget that y' is just a slope in tangent equation which has a form y - y_0 = y' (x -x_0)