`f(x) = sin(x)/(x^3)` Find the derivative of the trigonometric function.

Textbook Question

Chapter 2, 2.3 - Problem 42 - 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 ; where n = constant ; 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^3`

`f'(x) = [cosx*x^3 - 3x^2*sinx]/x^6`

`or, f'(x) = x^2[xcosx - 3sinx]/x^6`

`or, f'(x) = [xcosx-3sinx]/x^4`

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