Issolvi tan(θ)

$$\tan ( \theta )$$

Iddifferenzja w.r.t. θ

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Uża d-definizzjoni ta' tangent.

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

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.

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

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

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

Issimplifika.

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

Uża l-Pythagorean Identity.

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

Uża d-definizzjoni ta' secant.

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

Evalwa

$$\tan(\theta )$$