Find `(dy)/(dx),` `y=e^(3x)sin4x. 2^x`

Explanation

Let `y=e^{3 x} sin 4 x 2^{x}`

Take log both sides:


`Rightarrow log y=log (e^{3 x} sin 4 x 2^{x}) `

`Rightarrow log y=log (e^{3 x})+log (sin 4 x)+log (2^{x}) `

`{log (a b)=log a+log b ; log (frac{a}{b})=log a-log b} `

`Rightarrow log y=3 x log e+log (sin 4 x)+x log 2{log x^{a}=a log x} `

`Rightarrow log y=3 x+log (sin 4 x)+x log 2{log e=1}`
...