0

Guest

Courses New

Find out the derivtive of (sin x)/x using the first principle of derivative.

Find out the derivtive of (sin x)/x using the first principle of derivative.

Grade:11

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin

 

Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More