Differentiate each of the following from first principle: `(sin x)/x`

Explanation

`f(x)=(sin x)/x`



`f’(x)=lim_(h->0) (f(x+h)-f(x))/(h)`


`f’(x)=lim_(h->0) ((sin (x+h))/(x+h)-(sin x)/x)/(h)`


`f’(x)=lim_(h->0) ((xsin (x+h))-(x+h)(sin x))/(xh(x+h))`


`f’(x)=lim_(h->0) ((xsin (x+h)-xsinx-hsinx))/(xh(x+h))`


`f’(x)=lim_(h->0) ((x(sin (x+h)-sinx)-hsinx))/(xh(x+h))`


`f’(x)=lim_(h->0) (x(2cos (x+h/2)sin(h/2))-hsinx)/(xh(x+h))`


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