Find a formula for the derivative of the function
![\[ f(x) = \frac{1}{x^2+1} + x^5 \cos x. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-a08695c8b6293faf1d62d5e0bca314b2_l3.png "Rendered by QuickLaTeX.com")
Using the product rule for derivatives and the formulas for derivatives of quotients, polynomials, and cosine, we have
![\[ f'(x) = \frac{-2x}{(x^2+1)^2} + 5x^4 \cos x - x^5 \sin x. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-4b0526baaeb1cd0711b0feaa30c29f94_l3.png "Rendered by QuickLaTeX.com")
Find a formula for the derivative of the function
Using the product rule for derivatives and the formulas for derivatives of quotients, polynomials, and cosine, we have