Derivative of basic functions:

$$y=x^n : y^{\text{'}}=n·x^{n-1}$$

$$y=\sqrt{x} ; y^{\text{'}}=\frac{1}{2\sqrt{x}}$$

$$y=a^x ; y^{\text{'}}=a^x·\ln a$$

$$y=C·f\left(x\right) ; y^{\text{'}}=C·f\left(x\right)$$

Derivative of complex functions:

$$\frac{d}{dx}\left[f\left(g\left(x\right)\right)\right]=\frac{df}{dg}·\frac{dg}{dx}=f_g^{\text{'}}·g_x^{\text{'}}$$