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Please note that this solution is easier to explain with 2 diagrams 

The side opposite of the 30 degree angle: 

If we have the hypotenuse and require the length of the opposite side then we ...

 y = ln(2x+3 / 7x^3 +1)

d/dx(2x+3 / 7x^3 + 1) by quotient rule which is(v.du/dx - u.dv/dx) / v^2  where u=2x+3 and v=7x^3 +1   gives (-27x^3 -63x^2 +2) / (7x^3 +1)^2

so d/dx(ln(2x+3 / 7x^3 +...