💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



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} $



More Answers


You must be signed in to discuss.

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.