Question

y= ln(x^3 e^2x) (dy)/(dx)​

Answer 1

Answer:

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

divide by In :

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

find dy/dx:

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

Answer 2

Answer:

2 + 3/x.

Step-by-step explanation:

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

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

= 2 + 3/x.