Differentiate the function. f(x) = 2x ln(3x) - 2x

Question

Please help me 

Answer 1

This is a bunch of product and chain rules...

 

f'(x) = 2x * d/dx[ ln(3x) ] + d/dx [2x] * ln (3x) + d/dx ( -2x)

 

f'(x) = 2x * (1/3x) * d/dx(3x) + 2 * ln(3x) -2

 

f'(x) = (2x/3x) * 3 + 2 * ln(3x) - 2 

 

= 2 + 2ln(3x) - 2

 

= 2ln(3x)