How do you find the derivatives of #y=(5x-2)^3(6x+1)^2# by logarithmic differentiation?

1 Answer
WADU HEK
Apr 14, 2018

# y' = (5x-2)^3(6x+1)^2 ##((15)/(5x-2)+(12)/(6x+1))#

Explanation:

1/ ln(y) = #3ln(5x-2) + 2ln(6x+1)#
2/ #(1)/(y) y'# = #(3)((1)/(5x-2))(5) + (2)((1)/(6x+1))(6)#

3/ #(1)/(y) y'# = #(15)/(5x-2) + (12)/(6x+1)#

4/ y' = y#((15)/(5x-2) + (12)/(6x+1))#

5/ y' = #(5x-2)^3(6x+1)^2##((15)/(5x-2) + (12)/(6x+1))#

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