`(dy)/(dx)=(x(6\ cos 3x)-(2\ sin 3x)(1))/x^2`

`=(6x\ cos 3x-2\ sin 3x)/x^2`

When `x = 0.15` (in radians, of course), this expression (which gives us the slope) equals `-2.65`.

Here is a graph of our situation. The tangent to the curve at the point where `x=0.15` is shown. Its slope is `-2.65`.

Graph of tangent to a curve