Question

Consider the curve y=ln(3x-1) Let P be the point on the curve where x = 2.
(a) Write down the gradient of the curve at P.

(the anser is 0.6 but idk how they got there)

Answer 1

$y = \ln(3x-1) \\ \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{3x-1}\cdot 3 = \frac{3}{3x-1}$

$x=2$, so the gradient of this curve at $P$ is $\frac{3}{3\cdot 2-1} = \frac{3}{6-1} = \frac{3}{5} = 0.6$.