Solution 1.1:2b

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The expression is a sum of two terms which we differentiate one by one,

\displaystyle \begin{align}

f^{\,\prime}(x) &= \frac{d}{dx}\,\bigl(\cos x-\sin x\bigr)\\[5pt] &= \frac{d}{dx}\,\cos x - \frac{d}{dx}\,\sin x\\[5pt] &= -\sin x-\cos x\,\textrm{.} \end{align}