Derivative of basic functions:

$$y=x^n : y^{\text{'}}=n·x^{n-1}$$

$$y=\sin x ; y^{\text{'}}=\cos x$$

$$y=\cos x ; y^{\text{'}}=-\sin x$$

$$y=a^x ; y^{\text{'}}=a^x·\ln a$$

Derivative of complex functions:

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

Derivation of Product:

$$y=u·v : y^{\text{'}}=u^{\text{'}}·v+u·v^{\text{'}}$$

Derivation of Ratio:

$$y=\frac{u}{v} : y^{\text{'}}=\frac{u^{\text{'}}·v-u·v^{\text{'}}}{v^2}$$