$y=12-x+x^{-1}$ $\dfrac{dy}{dx}=0-1\times x^{1-1}-1\times x^{-1-1}$ $\dfrac{dy}{dx}=1-x^{-2}$ $\dfrac{d^{2}y}{dx^{2}}=0-2\times -x^{-2-1}$ $\dfrac{d^{2}y}{dx^{2}}=2x^{-3}$ $\dfrac{d^{2}y}{dx^{2}}=\dfrac{2}{x^{3}}$

$y=\dfrac{3}{2}x^{-1}$ $\dfrac{dy}{dx}=-1\times \dfrac{3}{2}x^{-1-1}$ $\dfrac{dy}{dx}=-\dfrac{3}{2}x^{-2}$ $\dfrac{dy}{dx}=-\dfrac{3}{2x^{2}}$ $\dfrac{d^{2}y}{dx^{2}}=-2\times -\dfrac{3}{2}x^{-2-1}$ $\dfrac{d^{2}y}{dx^{2}}=3x^{-3}$ $\dfrac{d^{2}y}{dx^{2}}=\dfrac{3}{x^{3}}$

$y=2x^{3}-x+7$ $\dfrac{dy}{dx}=3\times 2x^{3-1}-1\times x^{1-1}+0$ $\dfrac{dy}{dx}=6x^{2}-x^{0}$ $\dfrac{dy}{dx}=6x^{2}-1$ $\dfrac{d^{2}y}{dx^{2}}=2\times 6x^{2-1}-0\times x^{0-1}$ $\dfrac{d^{2}y}{dx^{2}}=12x$

$y=3x^{2}-x$ $\dfrac{dy}{dx}=2\times 3x^{2-1}-1\times x^{1-1}$ $\dfrac{dy}{dx}=6x^{1}-x^{0}$ $\dfrac{dy}{dx}=6x-1$ $\dfrac{d^{2}y}{dx^{2}}=1\times 6x^{1-1}-0\times x^{0-1}$ $\dfrac{d^{2}y}{dx^{2}}=6$

$y=2x^{5}+4x^{4}-3x^{3}+2x^{2}-7$ $\dfrac{dy}{dx}=5\times 2x^{5-1}+4\times 4x^{4-1}-3\times 3x^{3-1}+2\times 2x^{2-1}-0$ $\dfrac{dy}{dx}=10x^{4}+16x^{3}-9x^{2}+4x$