Question

What is the first derivative of a complex surge function?

this is the complex surge function `y=kx^a e^(-bx)` where a, b, k are positive constants.

Answer 1

`y'(x)=akx^(a-1)e^(-bx)-bkx^a*e^(-bx)`

Explanation:

use the product rule
[`d/dx(f(x)g(x))=f'(x)g(x)+f(x)g'(x)`]

`y'(x)=d/dx(kx^a)*(e^(-bx))+kx^a*d/dx(e^(-bx))`
`y'(x)=akx^(a-1)e^(-bx)+kx^a*e^(-bx)(-b)`
`y'(x)=akx^(a-1)e^(-bx)-bkx^a*e^(-bx)`

could also equal:
`y'(x)=kx^(a-1)e^(-bx)(a-bx)`