Question

How do you differentiate `y =( ln(3x + 2))^2` using the chain rule?

Answer 1

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

Explanation:

Differentiate using the `color(blue)( " chain rule")`

`y = [ln(3x + 2 ) ]^2`

`dy/dx = 2ln(3x+ 2 ) d/dx (ln(3x+ 2))`

`= 2ln(3x + 2 ) . 1/(3x + 2 ) d/dx (3x + 2 )`

`= 2ln(3x + 2 ) . 1/(3x + 2 ). 3`

`=( 6ln(3x + 2 ))/(3x + 2 )`