d/dθleft(cos(θ)right) eching

$$\frac{d}{d \theta } \left( \cos ( \theta ) \right)$$

Baholash

$$-\sin(\theta )$$

Derivativ ifodasidan foydalanish qadamlari

f\left(x\right) funksiyasi uchun, hosilasi \frac{f\left(x+h\right)-f\left(x\right)}{h} cheklovidir, chunki ana shu cheklov mavjud bo'lsa, h 0'ga o'tadi.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(\cos(\theta ))=\left(\lim_{h\to 0}\frac{\cos(\theta +h)-\cos(\theta )}{h}\right)$$

Kosinus uchun yig'indi formulasidan foydalanish.

$$\lim_{h\to 0}\frac{\cos(h+\theta )-\cos(\theta )}{h}$$

\cos(\theta ) omili.

$$\lim_{h\to 0}\frac{\cos(\theta )\left(\cos(h)-1\right)-\sin(\theta )\sin(h)}{h}$$

Chegarani qayta yozish.

$$\left(\lim_{h\to 0}\cos(\theta )\right)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\left(\lim_{h\to 0}\sin(\theta )\right)\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)$$

Limitlar h dan 0 sifatida hisoblanganda \theta ni konstanta sifatida foydalanish.

$$\cos(\theta )\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\sin(\theta )\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)$$

\lim_{\theta \to 0}\frac{\sin(\theta )}{\theta } chegarasi 1 dir.

$$\cos(\theta )\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\sin(\theta )$$

\lim_{h\to 0}\frac{\cos(h)-1}{h} chegarasini baholash uchun, avval surat va maxrajni \cos(h)+1 ga ko'paytiring.

$$\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)=\left(\lim_{h\to 0}\frac{\left(\cos(h)-1\right)\left(\cos(h)+1\right)}{h\left(\cos(h)+1\right)}\right)$$

\cos(h)+1 ni \cos(h)-1 marotabaga ko'paytirish.

$$\lim_{h\to 0}\frac{\left(\cos(h)\right)^{2}-1}{h\left(\cos(h)+1\right)}$$

Pifagor ayniyatidan foydalanish.

$$\lim_{h\to 0}-\frac{\left(\sin(h)\right)^{2}}{h\left(\cos(h)+1\right)}$$

Chegarani qayta yozish.

$$\left(\lim_{h\to 0}-\frac{\sin(h)}{h}\right)\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)$$

\lim_{\theta \to 0}\frac{\sin(\theta )}{\theta } chegarasi 1 dir.

$$-\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)$$

\frac{\sin(h)}{\cos(h)+1} 0 da davomiy sifatida foydalanish.

$$\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)=0$$

0 qiymatini \cos(\theta )\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\sin(\theta ) ifodasiga almashtirish.

$$-\sin(\theta )$$

θ ga nisbatan hosilani topish

$$-\cos(\theta )$$