find \\( \\frac { d y } { d x } \\) for \\( y = - 7 x + 3 \\cos x \\).\n\\( \\frac { d } { d x } ( - 7 x + 3…

Explanation:

Step1: Differentiate term -7x

Use the power rule (\frac{d}{dx}(ax^n)=anx^{n - 1}). For (y=-7x=-7x^1), (\frac{d}{dx}(-7x)=-7\times1\times x^{1 - 1}=-7).

Step2: Differentiate term 3cosx

Use the rule (\frac{d}{dx}(a\cos x)=-a\sin x). For (y = 3\cos x), (\frac{d}{dx}(3\cos x)=3\times(-\sin x)=-3\sin x).

Step3: Apply the sum rule of differentiation

If (y = u + v), then (\frac{dy}{dx}=\frac{du}{dx}+\frac{dv}{dx}). Here (u=-7x) and (v = 3\cos x). So (\frac{d}{dx}(-7x + 3\cos x)=\frac{d}{dx}(-7x)+\frac{d}{dx}(3\cos x)).

Answer:

(-7-3\sin x)