[MO412] Quizz Question 4

Mark the alternative that corresponds to the following derivates: $f(x) = 5x^{4} + 6x^{3} + 20$, $z(x) = 5x^{5} + \sqrt{x^{3}} - x^{\frac{3}{5}} $, and $g(x) = -\frac{1}{3}x^{15} + \frac{1}{\sqrt{x}} -\frac{3}{\sqrt[3]{x}} $ 

a) $f'(x) = 20x^{3} + 18x^{2}$; $z'(x) = 25x^{4} + \frac{3\sqrt{x}}{2} - \frac{3}{5}x^{-\frac{2}{5}} $;  $g'(x) = -5x^{14} - \frac{1}{2}x^{-\frac{3}{2}} - x^{-\frac{4}{3}}$  

b) $f'(x) = 20x^{3} - 18x^{2}$; $z'(x) = 25x^{4} - \frac{3\sqrt{x}}{2} + \frac{3}{5}x^{\frac{2}{5}} $;  $g'(x) = 5x^{14} + \frac{1}{2}x^{\frac{3}{2}} + x^{-\frac{4}{3}}$  

c) $f'(x) = 20x^{3} + 18x^{2}$; $z'(x) = 25x^{4} + \frac{3\sqrt{x}}{2} + \frac{3}{5}x^{\frac{2}{5}} $;  $g'(x) = -5x^{14} - 1x^{\frac{3}{2}} - x^{-\frac{4}{3}}$  

d) $f'(x) = 20x^{3} + 18x^{2}$; $z'(x) = 25x^{4} - \frac{\sqrt{x}}{2} - \frac{3}{5}x^{-\frac{2}{5}} $;  $g'(x) = -5x^{14} - \frac{1}{2}x^{3} - x^{\frac{4}{3}}$  

e) None of the above

Original Idea by: Levy Chaves