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Find the Derivative

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28. f(x) = (x3 + 3x + 2)/(x2 + 1)

32. f(x) = (cube root of x)(square root of x + 3)

14. f(x) = (x2 - 2x + 1)(x3 - 1)

18. (sinx)/x

20. f(x) = cosx/ex

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Solution Preview

28. f(x) = x3 + 3x + 2
x2 + 1

For this problem, remember that the derivative of a rational function f(x)/g(x) is g(x)f'(x) - f(x)g'(x)
[g(x)]2

f(x) = x3 + 3x + 2
x2 + 1

f'(x) = (x2 + 1)(3x2 + 3) - (x3 + 3x + 2)(2x)
(x2 + 1)(x2 + 1)

f'(x) = (3x4 + 6x2 + 3) - (2x4 + 6x2 + 4x)
(x2 + 1)(x2 + 1)

f'(x) = x4 - 4x + 3
(x2 + 1)(x2 + ...

Solution Summary

The solution uses the quotient rule and the power rule to find the derivatives of five functions.

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