`y = (e^-x (cos(x))^2)/(x^2 + x +1)` Use logarithmic differentiation to find the derivative of the function.

Textbook Question

Chapter 3, 3.6 - Problem 40 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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Taking the natural logarithm of both sides and applying the properties of logarithms, we get
`logy=loge^-x+2logcosx -log(x^2+x+1)`
Differentiating both sides with respect to x, we get
`1/y dy/(dx)=-1+(2/cosx)(-sinx) -(1/(x^2+x+1))(2x+1)`
`1/y dy/(dx)=-1-2tanx-(2x+1)/(x^2+x+1)`

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