Nilaikan
\cos(x)
Bezakan w.r.t. x
-\sin(x)
Kongsi
Disalin ke papan klip
\frac{\mathrm{d}}{\mathrm{d}x}(\sin(x))=\left(\lim_{h\to 0}\frac{\sin(x+h)-\sin(x)}{h}\right)
Bagi fungsi f\left(x\right), terbitannya adalah had bagi \frac{f\left(x+h\right)-f\left(x\right)}{h} apabila h pergi ke 0, jika had tersebut wujud.
\lim_{h\to 0}\frac{\sin(x+h)-\sin(x)}{h}
Gunakan Formula Hasil Tambah untuk Sinus.
\lim_{h\to 0}\frac{\sin(x)\left(\cos(h)-1\right)+\cos(x)\sin(h)}{h}
Faktorkan \sin(x).
\left(\lim_{h\to 0}\sin(x)\right)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\left(\lim_{h\to 0}\cos(x)\right)\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)
Tulis semula had.
\sin(x)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(x)\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)
Gunakan fakta bahawa x ialah pemalar apabila mengira had semasa h pergi ke 0.
\sin(x)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(x)
Had \lim_{x\to 0}\frac{\sin(x)}{x} ialah 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)
Untuk menilaikan had \lim_{h\to 0}\frac{\cos(h)-1}{h}, mula-mula darabkan pengangka dan penyebut dengan \cos(h)+1.
\lim_{h\to 0}\frac{\left(\cos(h)\right)^{2}-1}{h\left(\cos(h)+1\right)}
Darabkan \cos(h)+1 kali \cos(h)-1.
\lim_{h\to 0}-\frac{\left(\sin(h)\right)^{2}}{h\left(\cos(h)+1\right)}
Gunakan Identiti Phythagoras.
\left(\lim_{h\to 0}-\frac{\sin(h)}{h}\right)\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)
Tulis semula had.
-\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)
Had \lim_{x\to 0}\frac{\sin(x)}{x} ialah 1.
\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)=0
Gunakan fakta bahawa \frac{\sin(h)}{\cos(h)+1} adalah selanjar pada 0.
\cos(x)
Gantikan nilai 0 ke dalam ungkapan \sin(x)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(x).
Contoh
Persamaan kuadratik
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometri
4 \sin \theta \cos \theta = 2 \sin \theta
Persamaan linear
y = 3x + 4
Aritmetik
699 * 533
Matriks
\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]
Persamaan serentak
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Pembezaan
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Pengamiran
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Had
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}