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

f r o m f i r s t p r i n c i p l e o b t a i n t h e

d i f f r e n t i a l c o e f f i c i e n t o f c o s (x)

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

\frac{d y}{d x} = \lim_{h \to 0} \frac{f (x + h) - f (x)}{h} = \lim_{h \to 0} \frac{c o s (x + h) - c o s x}{h}

\frac{d (c o s x)}{d x} = \lim_{h \to 0} \frac{2 s i n (x + \frac{h}{2})}{\frac{h}{2} \times 2} \times (- s i n \frac{h}{2})

= s i n (x + \frac{0}{2}) \times - 1 = - s i n x