Question

How do you differentiate `f(x)=ln2x * tan3x` using the product rule?

Answer 1

I found: `f'(x)=tan(3x)/x+(3ln(2x))/cos^2(3x)`

Explanation:

The Product Rule tells us that if we a function `f` that is the product of 2 other functions:
`f(x)=g(x)*h(x)`
differentiating we get:
`f'(x)=g'(x)h(x)+g(x)h'(x)`
in our case:
`f'(x)=2/(2x)tan(3x)+ln(2x)1/cos^2(3x)*3`
Where I used the Chain Rule to differentiate each component function;
finally:
`f'(x)=tan(3x)/x+(3ln(2x))/cos^2(3x)`