How do you differentiate #g(y) =(1-2x^2)e^(7-x) # using the product rule?

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Answer 1 · 2017-09-11T16:26:17

#y'=e^(7-x)(2x^2+4x-1)#

#y=uv=>y'=color(red)(u')v+color(red)(u)v'#

#y=(1-2x^2)e^(7-x)#

#color(red)(u=1-2x^2=>u'=-4x)#

#v=e^(7-x)=>v'=-e^(7-x)#

#y'=color(red)(-4x)e^(7-x)+color(red)((1-2x^2))(-e^(7-x))#

#y'=-e^(7-x)(-4x+(1-2x^2))#

#y'=-e^(7-x)(-2x^2-4x+1)#

#y'=e^(7-x)(2x^2+4x-1)#