`f(x) = sin(x)/x, c=pi/6` Find f'(x) and f'(c).

Textbook Question

Chapter 2, 2.3 - Problem 18 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- 1) If y = sinx; then dy/dx = cosx

2) If y = x^n ; then dy/dx = n*x^(n-1)

3) If y = u/v ; where u & v are functions of 'x'; then dy/dx = [vu' - uv']/(v^2)

Now, 

`f(x) = sinx/x`

`or, f'(x) = [x*cosx - sinx]/x^2`

`or, f'(c) = f'(pi/6) = [(pi/6)cos(pi/6)-sin(pi/6)]/(pi/6)^2`

`or, f'(pi/6) = [(pi/6)*{sqrt(3)/2}-(1/2)]/(pi/6)^2`

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