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Abhingya Patra Grade: 11
        Find out the derivtive of (sin x)/x using the first principle of derivative.
7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Abhingya


let f(x) = (sinx)/x


so f(x+h) =(sin (x+h))/(x+h)


 


fo f'(x) = Lt h→0 {f(x+h) -f(x)} /h


          = Lt h→0 {(sin (x+h))/(x+h )  - (sinx)/x } /h


          =Lt h→0 {xsin (x+h)   - (x+h)sinx } /hx(x+h)


          =Lt h→0 {x(sin (x+h)   - sinx } /hx(x+h)    - Lt h→0hsinx /hx(x+h)


          use sinC -sinD formula


          =Lt h→0 {2(cos (x+h/2)  sin(h/2) } /h(x+h)    - Lt h→0hsinx /hx(x+h)


         now open series for sin(h/2) and apply limit


 f'(x) = cos(x) /x  - sin(x) /x2



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Regards,
Askiitians Experts
Badiuddin


 

7 years ago
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