Question

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Answer 1

$a) \frac{d}{dx} = 21x {}^{20}$


$b) \frac{d}{dx} = 20x {}^{3} + 6x {}^{2}$


$c) \frac{d}{dy} = 15y {}^{2} + 60y {}^{4} - 12y {}^{3}$


$d) \frac{d}{dx} = \frac{1}{2} (x {}^{3} - 4x {}^{2} + 7) {}^{ - \frac{1}{2} } (3x {}^{2} - 8x) \\ \frac{d}{dx} = \frac{3x {}^{2} - 8x }{ 2\sqrt{x {}^{3} - 4x {}^{2} - 7} }$


$e) \frac{d}{dx} = \frac{(6x )(2x - 1) - (2)(3x {}^{2} + 2)}{(2x - 1) {}^{2} } \\ \frac{d}{dx} = \frac{12x {}^{2} - 6x - 6x {}^{2} - 4}{(2x -1 ) {}^{2} } \\ \frac{d}{dx} = \frac{6x {}^{2} - 6x - 4}{(2x - 1) {}^{2} }$