Calculate dy/dx if y = Ln (2x3 + 3x).

Differentiate using the chain rule:

d/du [ln (u) ] d/dx[2x^3+3x]

derivative of ln (u) = 1/u

1/u d/dx[2x^3+3x]

1/2x^3+3x d/dx[2x^3+3x]

Differentiate

(6x^2+3) 1/2x^3+3x

Simplify

Dy/dx = 3 (2x^2+1) / x (2x^2 + 3)