5-20 Find $f'(x)$. 5. $f(x) = (3x^2+6)(2x-\frac{1}{4})$ 6. $f(x) = (2 - x - 3x^3)(7 + x^5)$ 7. $f(x) = (x^3 + 7x^2 - 8)(2x^{-3} + x^{-4})$ 8. $f(x) = (\frac{1}{x} + \frac{1}{x^2})(3x^3 + 27)$ 9. $f(x) = (x - 2)(x^2 + 2x + 4)$ 10. $f(x) = (x^2 + x)(x^2 - x)$ 11. $f(x) = \frac{3x + 4}{x^2 + 1}$ 12. $f(x) = \frac{x - 2}{x^4 + x + 1}$ 13. $f(x) = \frac{x^2}{3x - 4}$ 14. $f(x) = \frac{2x^2 + 5}{3x - 4}$ 15. $f(x) = \frac{(2\sqrt{x} + 1)(x - 1)}{x + 3}$ 16. $f(x) = (2\sqrt{x} + 1)(\frac{2 - x}{x^2 + 3x})$ 17. $f(x) = (2x + 1)(1 + \frac{1}{x})(x^{-3} + 7)$ 18. $f(x) = x^{-5}(x^2 + 2x)(4 - 3x)(2x^9 + 1)$ 19. $f(x) = (x^7 + 2x - 3)^3$ 20. $f(x) = (x^2 + 1)^4$
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The product rule states that the derivative of a product of two functions is equal to the first function times the derivative of the second function plus the second function times the derivative of the first function. In this case, the first function is $3x^2 + 6$ Show more…
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