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

1 Answer
Jan 31, 2016

Answer:

# 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 ) #