What is the first derivative of a complex surge function?

Question

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

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Answer 1 · 2018-04-14T03:01:25

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

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:
$y'(x)=kx^(a-1)e^(-bx)(a-bx)$