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Problem 56 Hard Difficulty

Use the method of Exercise 55 to compute $ Q'(0). $ where

$ Q(x) = \frac {1 + x + x^2 + xe^x }{1 - x + x ^2 - xe^x} $

Answer

4

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Video Transcript

Hey, it's Claire is suing you right here. So we're gonna use the method of exercise 55 to get que the derivative of Q of zero and cue of accessible to warn. Plus acts plus x square plus X e x all over one minus next, plus X square minus X e to the X. So for EPA backs, we got one plus thanks. Bless Square plus X B to the X, which is the numerator. So when we derive this, we get zero plus one plus two x plus x Eat the X bless one times e to the X for G of X. You make this equal to the denominator, which is one minus x less X square minus x Eat the X. The derivative is equal to zero minus one less to x minus X e to the X minus one times E to the X. That's zero. It comes one, and the derivative of F of zero equals two. Fergie of zero. It's one, and the derivative of G 00 is too. So the derivative of F, divided by G. 00 is equal to G turns the derivative of minus f times the derivative of G over G Square. Look that only at one times to burn us more in terms negative too. All over one square equals four.