Baholash
-\sin(\theta )
θ ga nisbatan hosilani topish
-\cos(\theta )
Baham ko'rish
Klipbordga nusxa olish
\frac{\mathrm{d}}{\mathrm{d}\theta }(\cos(\theta ))=\left(\lim_{h\to 0}\frac{\cos(\theta +h)-\cos(\theta )}{h}\right)
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.
\lim_{h\to 0}\frac{\cos(h+\theta )-\cos(\theta )}{h}
Kosinus uchun yig'indi formulasidan foydalanish.
\lim_{h\to 0}\frac{\cos(\theta )\left(\cos(h)-1\right)-\sin(\theta )\sin(h)}{h}
\cos(\theta ) omili.
\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)
Chegarani qayta yozish.
\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)
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 )
\lim_{\theta \to 0}\frac{\sin(\theta )}{\theta } chegarasi 1 dir.
\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)
\lim_{h\to 0}\frac{\cos(h)-1}{h} chegarasini baholash uchun, avval surat va maxrajni \cos(h)+1 ga ko'paytiring.
\lim_{h\to 0}\frac{\left(\cos(h)\right)^{2}-1}{h\left(\cos(h)+1\right)}
\cos(h)+1 ni \cos(h)-1 marotabaga ko'paytirish.
\lim_{h\to 0}-\frac{\left(\sin(h)\right)^{2}}{h\left(\cos(h)+1\right)}
Pifagor ayniyatidan foydalanish.
\left(\lim_{h\to 0}-\frac{\sin(h)}{h}\right)\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)
Chegarani qayta yozish.
-\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)=0
\frac{\sin(h)}{\cos(h)+1} 0 da davomiy sifatida foydalanish.
-\sin(\theta )
0 qiymatini \cos(\theta )\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\sin(\theta ) ifodasiga almashtirish.
Misollar
Ikkilik tenglama
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometriya
4 \sin \theta \cos \theta = 2 \sin \theta
Chiziqli tenglama
y = 3x + 4
Arifmetik
699 * 533
Matritsa
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simli tenglama
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differensatsiya
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Oʻngga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Chegaralar
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}