Datrys cos(θ52)

$$\cos ( \theta 52 )$$

Gwahaniaethu w.r.t. θ_52

$$-\sin(\theta _{52})$$

Camau gan Ddefnyddio Diffiniad o Ddeilliad

Ar gyfer y ffwythiant f\left(x\right), y deilliad yw'r terfyn \frac{f\left(x+h\right)-f\left(x\right)}{h} gan fod h yn mynd i 0, os yw’r terfyn hwnnw yn bodoli.

$$\frac{\mathrm{d}}{\mathrm{d}\theta _{52}}(\cos(\theta _{52}))=\left(\lim_{h\to 0}\frac{\cos(\theta _{52}+h)-\cos(\theta _{52})}{h}\right)$$

Defnyddio’r Fformiwla Swm ar gyfer Cosin.

$$\lim_{h\to 0}\frac{\cos(h+\theta _{52})-\cos(\theta _{52})}{h}$$

Ffactora allan \cos(\theta _{52}).

$$\lim_{h\to 0}\frac{\cos(\theta _{52})\left(\cos(h)-1\right)-\sin(\theta _{52})\sin(h)}{h}$$

Ailysgrifennu’r terfyn.

$$\left(\lim_{h\to 0}\cos(\theta _{52})\right)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\left(\lim_{h\to 0}\sin(\theta _{52})\right)\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)$$

Defnyddio'r ffaith bod \theta _{52} yn gyson pan fydd terfynau cyfrifiadura fel h yn mynd i 0.

$$\cos(\theta _{52})\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\sin(\theta _{52})\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)$$

Y terfyn \lim_{\theta _{52}\to 0}\frac{\sin(\theta _{52})}{\theta _{52}} yw 1.

$$\cos(\theta _{52})\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\sin(\theta _{52})$$

I enrhifo’r terfyn \lim_{h\to 0}\frac{\cos(h)-1}{h}, yn gyntaf lluoswch y rhifiadur a'r enwadur â \cos(h)+1.

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

Lluoswch \cos(h)+1 â \cos(h)-1.

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

Defnyddio'r Hunaniaeth Pythagoreaidd.

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

Ailysgrifennu’r terfyn.

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

Y terfyn \lim_{\theta _{52}\to 0}\frac{\sin(\theta _{52})}{\theta _{52}} yw 1.

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

Defnyddio'r ffaith fod \frac{\sin(h)}{\cos(h)+1} yn barhaus yn 0.

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

Amnewid y gwerth 0 i mewn i’r mynegiad \cos(\theta _{52})\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)-\sin(\theta _{52}).

$$-\sin(\theta _{52})$$

Enrhifo

$$\cos(\theta _{52})$$