Issolvi tanalpha

$$\tan \alpha$$

Iddifferenzja w.r.t. α

$$\frac{1}{\left(\cos(\alpha )\right)^{2}}$$

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Uża d-definizzjoni ta' tangent.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha }(\frac{\sin(\alpha )}{\cos(\alpha )})$$

Għal kwalunkwe żewġ funzjonijiet differenzjabbli, id-derivattiv tal-kwozjent ta' żewġ funzjonijiet huwa d-denominatur immultiplikat bid-derivattiv tan-numeratur minus in-numeratur immultiplikat bid-derivattiv tad-denominatur, kollha diviżi bid-denominatur kwadrat.

$$\frac{\cos(\alpha )\frac{\mathrm{d}}{\mathrm{d}\alpha }(\sin(\alpha ))-\sin(\alpha )\frac{\mathrm{d}}{\mathrm{d}\alpha }(\cos(\alpha ))}{\left(\cos(\alpha )\right)^{2}}$$

Id-derivattiv ta' sin(\alpha ) hu cos(\alpha ), u d-derivattiv ta' cos(\alpha ) huwa −sin(\alpha ).

$$\frac{\cos(\alpha )\cos(\alpha )-\sin(\alpha )\left(-\sin(\alpha )\right)}{\left(\cos(\alpha )\right)^{2}}$$

Issimplifika.

$$\frac{\left(\cos(\alpha )\right)^{2}+\left(\sin(\alpha )\right)^{2}}{\left(\cos(\alpha )\right)^{2}}$$

Uża l-Pythagorean Identity.

$$\frac{1}{\left(\cos(\alpha )\right)^{2}}$$

Uża d-definizzjoni ta' secant.

$$\left(\sec(\alpha )\right)^{2}$$

Evalwa

$$\tan(\alpha )$$