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Question Number 123147 by aurpeyz last updated on 23/Nov/20

$$fromfirstprincipleobtainthe$$$$diffrentialcoefficientofcos\left(x\right)$$

Answered by TANMAY PANACEA last updated on 23/Nov/20

$$\frac{dy}{dx}=\underset{h\to 0}{\lim }\frac{f(x+h)-f\left(x\right)}{h}=\underset{h\to 0}{\lim }\frac{cos(x+h)-cosx}{h}$$$$\frac{d\left(cosx\right)}{dx}=\underset{h\to 0}{\lim }\frac{2sin(x+\frac{h}{2})}{\frac{h}{2}\times 2}\times (-sin\frac{h}{2})$$$$=sin(x+\frac{0}{2})\times -1=-sinx$$

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