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hpfan101
 one year ago
Differentiate:
\[\frac{ x^2e^x }{ x^2+e^x }\]
hpfan101
 one year ago
Differentiate: \[\frac{ x^2e^x }{ x^2+e^x }\]

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 one year ago
Best ResponseYou've already chosen the best response.1Are you familiar with the quotient rule?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\left(\frac uv\right)' = \frac{u'vuv'}{v^2}\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2@hpfan101, can you identify \(u\) and \(v\)? can you find the derivatives \(u'\) and \(v'\)?

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.1I'm somewhat familiar with the quotient rule.

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.1Would it be: \[\frac{ (x^2e^x)'(x^2+e^x)(x^2e^x)(x^2+e^x)' }{ (x^2+e^x)^2 }\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yeah, that's right, now simplify those derivatives

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.1Okay, what I'm not sure about is the first set we would find the derivative of. Would the derivative of \[(x^2e^x)'\] be \[2xe^x\]?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2use the product rule \[(fg)' = f'g+fg'\]

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.1Oh okay. So it would be: \[(x^2)'(e^x)+(x^2)(e^x)'= 2x(e^x)+x^2(e^x) =2xe^x+x^2e^x\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2that's right and if you factor it \(= (2x+x^2)e^x\)

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.1Oh okay! Thank you! I think I can figure out the rest.

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2to compute\[(x^2+e^x)'\] use the sum rule \[(a+b)'=a'+b'\]

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.1Okay, will do! Thanks!

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2NB: expanding the square in the denominator will not simplify your result (in this case)

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.1Ah, okay. I see. It'd be easier to leave the denominator how it is.
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