Question

How do you find the derivative of `f(x) = 3x^2 ln 2x`?

Answer 1

`f'(x)=(dy)/(dx)=6xln2x+3x`

Explanation:

we need to use the product rule

`d/(dx)(color(red)(u)v)=vcolor(red)((du)/(dx))+color(red)(u)(dv)/(dx)`

`d/(dx)(color(red)(3x^2)ln2x)`

`(dy)/(dx)=ln2xcolor(red)(d/(dx)(3x^2))+color(red)(3x^2)d/(dx)(ln2x)`

`(dy)/(dx)=ln2x xxcolor(red)( 6x)+color(red)(3x^2) xx 1/(2x)xx2`

`(dy)/(dx)=6xln2x+3x`