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If f(x) = x cos x, find f' (x)....

If `f(x) = x cos x`, find `f' (x)`.

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AI Generated Solution

To find the derivative of the function \( f(x) = x \cos x \), we will use the product rule of differentiation. The product rule states that if you have two functions \( u \) and \( v \), then the derivative of their product is given by: \[ f'(x) = u'v + uv' \] where \( u' \) is the derivative of \( u \) and \( v' \) is the derivative of \( v \). ...
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Knowledge Check

  • If f(x) = cos x, then

    A
    f(x) is strictly decreasing in `(0, pi)`
    B
    f(x) is strictly increasing in `(0, 2pi)`
    C
    f(x) is neither increasing nor decreasing in `(pi, 2pi)`
    D
    All the above are correct
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