Answer
$\cos x +\sin x$
Work Step by Step
We have: $f(x)=\sin x-\cos x$
We need to differentiate both sides with respect to $x$.
$\dfrac{d[f(x)]}{dx}= \dfrac{d(\sin x-\cos x)}{dx} \\ f^{\prime}(x)= \dfrac{d}{dx}(\sin x)- \dfrac{d}{dx}(\cos x)\\f^{\prime}(x)=\cos x-(-\sin x)$
Therefore, $f^{\prime}(x)=\cos x +\sin x$
