#y=x^3/e^x# what is y"?

#y=x^3/e^x# Find y". Simplify your answer

1 Answer
Andrea S.
Apr 19, 2018

#(d^2y)/dx^2 =( x^3 -6x^2 +6x)/e^x#

Explanation:

You can write the function also as:

#y= x^3e^(-x)#

and use the product rule:

#dy/dx = 3x^2e^(-x) -x^3e^(-x)#

#(d^2y)/dx^2 = 6xe^(-x)-3x^2e^(-x) -3x^2e^(-x) + x^3e^(-x)#

#(d^2y)/dx^2 =e^(-x)( 6x-6x^2 + x^3)#

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