Calculus question
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Differentiate the given functions. For this question, you may use the following differentiation rules and formulas:
If r is any rational number, then
d/dx (x^r) = rx^(r-1)
If f and g are differentiable functions of x, and if ? [alpha] and ? [beta] are constants, then
d/dx ( ?f(x) + ?g(x)) = ? d/dx (f(x)) + ? d/dx (g(x))
In each case, state the domain of the derivative.
a) f(x) = 2x^(3) - 3x^(2) + 2x - 3.
Answer: The derivative of f(x) is f[prime](x)=__________, and the domain of f[prime] is__________
(b) f(x)=1x^(3/2) + 5x^(1/2) - 5x^(-1/2) - 5x^(-3/2)
Answer: The derivative of f(x) is f[prime](x)=_________, and the domain of f[prime] is__________
(c) f(x) = -2(sqrt(x)) + 2/(sqrt(x)) + -2/x + 3/x^2
Answer: The derivative of f(x) is f[prime](x)=___________, and the domain of f[prime] is_________
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Solution Summary
The expert differentiates the given functions for rational numbers.
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