Question

Y= ln(x^3 e^2x) (dy)/(dx)​

Answer 1

2 + 3/x.

Explanation:

y = ln(x^3 . e^(2x)

dy/dx = 1 /(x^3 e^2x) * (2x^3e^(2x) + 3x^2 e ^(2x))

= 2 + 3/x.

Answer 2

`y = ln( {x}^(3) . {e}^(2x) )`

divide by In :

`(y)/( ln) = \frac{ ln( {x}^(3). {e}^(2x) ) }{ ln } \\ \\ {e}^(y) = {x}^(3) . {e}^(2x)`

find dy/dx:

`{d( {e}^(y)) } = ( {x}^(3) . {e}^(2x) )dx \\ {e}^(y) dy = \{(3 {x}^(2) . {e}^(2x) ) + ( {x}^(3) .2 {e}^(2x) ) \}dx \\ \\ {e}^(y) (dy)/(dx) = {x}^(3) + 3 {x}^(2) + 3 {e}^(2x) \\ \\ (dy)/(dx) = \frac{ {x}^(3) + 3 {x}^(2) + 3 {e}^(2x) }{ {e}^(y) } \\ \\ { \boxed{ \boxed{(dy)/(dx) = \frac{ {x}^(3) + 3 {x}^(2) + 3 {e}^(2x) }{ {e}^{ {x}^(3). {e}^(2x) } }}}}`