Question

j(x)=ln(2x+1)e^(3x)
Determine the derivative function.

Please help! I do not know where to begin.

Answer 1

Start by identifying what type function you have here. I see immediately that it's a product: the product of ln(2x+1) and e^(3x).

So, begin finding the derivative by applying the PRODUCT RULE.

Answer 2

And the product rule states
\[\large f(x)g'(x) + f'(x)g(x)\]

Let f(x) = ln(2x + 1)
and g(x) = e^(3x)

Answer 3

okay, f'(x)= [3e^(3x) \ln(2x+1) +(2e^(3x))/(2x+1)]

Does this look right?

Answer 4

Looks correct to me!