Lutasin ang tan(θ)

$$\tan ( \theta )$$

I-differentiate ang w.r.t. θ

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

Mga Hakbang sa Paggamit ng Derivative Rule for Quotient

Gamitin ang definition of tangent.

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

Para sa anumang dalawang madi-differentiate na function, ang derivative ng quotient ng dalawang function ay ang denominator times ang derivative ng numerator minus ang numerator times ang derivative ng denominator, lahat ng ito ay dini-divide ng denominator squared.

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

Ang derivative ng sin(\theta ) ay cos(\theta ), at ang derivative ng cos(\theta ) ay −sin(\theta ).

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

Pasimplehin.

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

Gamitin ang Pythagorean Identity.

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

Gamitin ang definition of secant.

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

I-evaluate

$$\tan(\theta )$$