Question

Математика 11 клас.

Відповідь повинна бути повною.

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Answer 1

$1)y = {6}x^{4} + 3x - 1 \\ \frac{d}{dx} (6 {x}^{4} + 3x - 1) = 24 {x}^{3} + 3 \\ 2)y = \sqrt[4]{ {x}^{3} } + 2x \\ \frac{d}{dx}(x {}^{ \frac{3}{4} } + 2x) = \frac{3}{4} x {}^{ - \frac{ 1}{4} } + 2 \\ 3)y = \sqrt{x} ( {x}^{2} + 5) \\ \frac{d}{dx}( {x}^{ \frac{1}{2} }( {x}^{2} + 5)) = \frac{d}{dx}x {}^{ \frac{1}{2} }(x {}^{2} + 5) + \frac{d}{dx}( {x}^{2} + 5) \sqrt{x} = \\ = \frac{1}{2}x {}^{ - \frac{1}{2} }( {x}^{2} + 5) + 2x \times \sqrt{x} = \frac{x {}^{ \frac{3}{2} } }{2} + \\ + \frac{5}{2 \sqrt{x} } + 2x {}^{ \frac{3}{2} } = \frac{5}{2} x {}^{ \frac{3}{2} } + \frac{5}{2 \sqrt{x} } \\ 4) y = \frac{2x}{x + 4} \\ \frac{d}{dx} ( \frac{2x}{x + 4} ) = \frac{ \frac{d}{dx}2x \times (x + 4) - 2x \times \frac{d}{dx}(x + 4) }{(x + 4) {}^{2} } = \frac{2(x + 4) - 2x}{(x + 1) {}^{2} } = \\ = \frac{2x + 8 - 2x}{( x+ 4) {}^{2} } = \frac{8}{(x + 4) {}^{2} }$