Question

What is the derivative of `f(x) = 3x^2 ln 2x`?

Answer 1

`d/dx ( 3x^2ln2x) = 3x( 1+ 2ln 2x )`

Explanation:

Using the product rule:

`d/dx ( 3x^2ln2x) = d/dx(3x^2)ln 2x + 3x^2 d/dx (ln2x)`

`d/dx ( 3x^2ln2x) = 6xln 2x + 3x^2 2/(2x)`

`d/dx ( 3x^2ln2x) = 6xln 2x + 3x`

`d/dx ( 3x^2ln2x) = 3x( 1+ 2ln 2x )`