求导：f(x)=(x-k)^2ex/k答案是f'(x)1/k(x^2-k^2)ex/k求详解…想了很久不会…ex/k意思是e的k分之x次方…谢谢…

Question

求导：f(x)=(x-k)^2ex/k 答案是f'(x)1/k(x^2-k^2)ex/k 求详解…想了很久不会…
ex/k意思是e的k分之x次方…谢谢…

Answer 1

f(x) = (x-k)^2 * e^(x/k)f'(x) = [ (x-k)^2 ] ' * e^(x/k) + (x-k)^2 * [ e^(x/k) ] '= 2(x-k) e^(x/k) + (x-k)^2 * e^(x/k) * 1/k= e^(x/k) * [ 2(x-k) + (x-k)^2 /k ]= e^(x/k) * (x^2 - k^2) / k