Differentiate each of the following functions. (Do not use the product rule and quotiate rule)

Question

a) f(x) = 2x^3 + (3) / (x^3) + 4∛(x) + (5) / (∛x)

b) f(x) = (3x - 2x√x)(7x + 2)

c) f(x) = (t^2 - 2t + 3) / 2t^2

Answer 1

OK, first of all your notation in the first part is unclear-- you have 2 division symbols--at least to me what you really mean is not clear. I suggest you re-submit that one with clearer notation (which, I admit, is hard with this editor).

In the second part, you can expand the product and then express the product of x√x as x^3/2 and then differentiate...that avoids the product rule.

In the 3rd part, you can do the division and write the fractions with t in the denominator as negative exponents...and that avoids the product and quotient rule.