`f(x) = xcos(x), c=pi/4` Find f'(x) and f'(c).

Textbook Question

Chapter 2, 2.3 - Problem 17 - 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 = cosx; then dy/dx = -sinx

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 = uv' + vu'

Now, 

`f(x) = xcos(x)`

`f'(x) = -xsin(x) + cos(x)`

`f'(c) = f'(pi/4) = -(pi/4)*sin(pi/4) + cos(pi/4) `

`or, f'(pi/4) = 0.152`

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