2.2 Differential Formulas

(a) $\displaystyle{\frac{dy}{dx} = \frac{1}{n}x^{\frac{1}{n} - 1}}$ (b) $\displaystyle{\frac{dy}{dx} = \frac{1}{2\sqrt{x}}}$

(a) $\displaystyle{y' = 4008x(x^{2} + 1)^{2003}}$ (b) $\displaystyle{y' = 6(x^{2} + \frac{1}{x^{2}})^{2}(x - \frac{1}{x^{3}})}$

(a) $\displaystyle{\frac{dy}{dx} = 2(x-1)}$ (b) $\displaystyle{\frac{dy}{dx} = - \frac{x}{y}}$

(a) $\displaystyle{2x\log{x} + x}$ (b) $\displaystyle{3x^{2}\sin{2x} + 2x^{3}\cos{2x}}$ (c) $\displaystyle{\frac{2}{\sqrt{1 - 4x^{2}}}}$ (d) $\displaystyle{\frac{e^{x}}{2\sqrt{e^{x} + 1}}}$

(e) $\displaystyle{3(\sin{(x+1)})^{2}\cos{(x+1)}}$ (f) $\displaystyle{\sin^{-1}(2x) + \frac{2x}{\sqrt{1 - 4x^{2}}}}$