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# Use logarithmic differentiation to find the derivative of the function.$y = \frac {e^{-x} \cos^2 x}{x^2 + x + 1}$

## $y^{\prime}=-\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1}\left[-1-2 \tan x-\frac{2 x+1}{x^{2}+x+1}\right]$

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

in this trouble ordering function. War as eternity extends Those I'm spared effects the wife by Extreme plus X Plus one. We asked you celebrating differentiation do with optional I celestic Nature Love boat size. Now we have functioned do either by their function using property. It's a little graphic functions. We can write this one as natural law Off eater, negative X treme Sports on spirit effects minus nation Law Expert plus X plus or here we have to function, multiply by each other. We can then further write this one as nation local Flying sea With the nation's law off, he's very negative. X plus nature Log of coastline spirit of X minus nation log of X rated X one. Make sure local beat your negative X This witness love me only will be left with Native X. Now let's take. They're both sides. We have my point while left inside under breakfast on me have negative one plus war over Cho San Spirit effects. Multiply by day with Coco Sanskrit effects, which is to throw Sinus turns negative. Sign X minus one over. Expect plus expose one month's bye bye Derek off that which is to experts Well, now we know the value. Why? So let's just want to play the right inside that beat and find out to s either Negative X temps, coats and spirit of X divided by expert plus X was warm times of days will cast a lot. With this form, you'll have costar Nixon Denominator. Negative sign next to WiFi Native Co. Sonics is negative. Off tensions affects what we have. Negative born minus form uh over eight scrape plus X plus one times X plus form minus two engines, off X.

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp