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} = (1)/(3x-1)\cdot 3 = (3)/(3x-1)`


`x=2`, so the gradient of this curve at
`P` is
`(3)/(3\cdot 2-1) = (3)/(6-1) = (3)/(5) = 0.6`.