Question

Differentiate e^{4x + 5} w.r..t.e^3x

Answer 1

Let u = e^{4x + 5} and v = e^3x

`(du)/dx = 4e^(4x + 5) and (dv)/dx = 3e^(3x)`

we have to find `(du)/(dv)`

`(du)/(dv) = ((du)/(dx))/((dv)/(dx)) = [4e^(4x + 5)]/[3e^(3x)]`

= `4/3e^( 4x + 5 - 3x)`

= `4/3e^( x + 5 )`

`therefore (du)/(dv) = 4/3e^( x + 5 )`