Question

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

Answer 1

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

Explanation:

`(dy)/(dx)`
`ln(x)=`
`(1)/(x)` .

Therefore:

`(dy)/(dx)`
`ln(2x^(3)+3x) = (1)/(2x^(3)+3x) *6x^2+3`

`6x^2+3` is multiplied because of the chain rule.

Answer 2

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)