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Iddifferenzja w.r.t. θ
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Problemi Simili mit-Tiftix tal-Web

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\frac{\mathrm{d}}{\mathrm{d}\theta }(\sin(\theta ))=\left(\lim_{h\to 0}\frac{\sin(\theta +h)-\sin(\theta )}{h}\right)
Għall-funzjoni f\left(x\right), id-derivattiv huwa l-limitu ta' \frac{f\left(x+h\right)-f\left(x\right)}{h} billi h jmur għal 0, jekk jeżisti dak il-limitu.
\lim_{h\to 0}\frac{\sin(h+\theta )-\sin(\theta )}{h}
Uża l-Formula tas-Somma għal Sine.
\lim_{h\to 0}\frac{\sin(\theta )\left(\cos(h)-1\right)+\cos(\theta )\sin(h)}{h}
Iffattura 'l barra \sin(\theta ).
\left(\lim_{h\to 0}\sin(\theta )\right)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\left(\lim_{h\to 0}\cos(\theta )\right)\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)
Erġa' ikteb il-limitu.
\sin(\theta )\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(\theta )\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)
Uża l-fatt li \theta huwa kostanti meta taħdem il-limiti bħala h jmorru għal 0.
\sin(\theta )\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(\theta )
Il-limitu \lim_{\theta \to 0}\frac{\sin(\theta )}{\theta } huwa 1.
\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)
Biex tevalwa l-limitu \lim_{h\to 0}\frac{\cos(h)-1}{h}, l-ewwel immultiplika n-numeratur u d-denominatur b'\cos(h)+1.
\lim_{h\to 0}\frac{\left(\cos(h)\right)^{2}-1}{h\left(\cos(h)+1\right)}
Immultiplika \cos(h)+1 b'\cos(h)-1.
\lim_{h\to 0}-\frac{\left(\sin(h)\right)^{2}}{h\left(\cos(h)+1\right)}
Uża l-Pythagorean Identity.
\left(\lim_{h\to 0}-\frac{\sin(h)}{h}\right)\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)
Erġa' ikteb il-limitu.
-\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)
Il-limitu \lim_{\theta \to 0}\frac{\sin(\theta )}{\theta } huwa 1.
\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)=0
Uża l-fatt li \frac{\sin(h)}{\cos(h)+1} huwa kontinwu f'0.
\cos(\theta )
Issostitwixxi l-valur 0 fl-espressjoni \sin(\theta )\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(\theta ).