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Find the derivative of cos x from fir...

Find the derivative of cos x from first principle.

Text Solution

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Let `f(x)=cos x`
`rArr f(x+h)=cos(x+h)`
`therefore f(x)=underset(hrarr0)"lim"(f(x+h)-f(x))/(h)`
`=underset(hrarr0)"lim"(cos(x+h)-cosx)/( h)`
`=underset(hrarr0)"lim"(-2sin(x+(h)/(2))sin(h)/(2))/(2.(h)/(2))=-sinx`.
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