Question

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С 9-14 задания

Answer 1

9) $\frac{d(\sin(\frac{\pi}{6}-x))}{dx} = = \frac{d(\frac{\pi}{6}-x)}{dx} \times \frac{d(\sin(\frac{\pi}{6}-x))}{d(\frac{\pi}{6}-x)} = -1 \times \cos(\frac{\pi}{6}-x)$

10) $\frac{d(\cos(-6x + 7))}{dx} = = \frac{d(-6x + 7)}{dx} \times \frac{d(\cos(-6x + 7))}{d(-6x + 7)} = -1 \times -\sin(-6x+7) = \sin(-6x+7)$

11) $\frac{d(3(e^x)^2-\sqrt{x})}{dx} = 3\frac{d((e^x)^2)}{dx} - \frac{d(\sqrt{x})}{dx} = 3 \times \frac{d(e^x)}{dx} \times \frac{d((e^x)^2)}{d(e^x)} + \frac{1}{2\sqrt{x}} = 3\times e^x \times 2e^x + \frac{1}{2\sqrt{x}} = 6e^2x + \frac{1}{2\sqrt{x}}$

12) $\frac{d(e^{x-1} \times x^8)}{dx} = \frac{d(e^{x-1})}{dx} \times x^8 + e^{x-1} \times \frac{d(x^8)}{dx} = e^{x-1} \times (x^8 + 8x^7)$

13) $\frac{d(e^{x} \times (x^3 - 5x + 3))}{dx} = e^x \times (x^3 - 5x + 3 - 3x^2 + 5) = e^x \times (x^3 -3x^2 - 5x + 8)$

14) $\frac{d(e^{2x} \times \sqrt{2x-3})}{dx} = 2e^{2x} \times \sqrt{2x-3} + e^{2x} \times \frac{2}{2\sqrt{2x-3}} = e^{2x} \times (2\sqrt{2x-3} + \frac{1}{\sqrt{2x-3}})$