How do you differentiate #f(x)=(x^3-2x)(e^x-x^2)# using the product rule?

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Answer 1 · 2016-07-03T15:54:26

#y = (x^3-2x)(e^x-x^2)#

#ln(y) = ln(x^3-2x) + ln(e^x-x^2)#

#(y')/y = (3x^2-2)/(x^3-2x)+(e^x-2x)/(e^x-x^2)#

#y'=y((3x^2-2)/(x^3-2x)+(e^x-2x)/(e^x-x^2))#

with #y = (x^3-2x)(e^x-x^2)#

it give you

#y'=(3x^2-2)(e^x-x^2)+(e^x-2x)(x^3-2x)#