If where is differentiable

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

If y=cos⁡(g(x))y=\cos(g(x)) where g(x)g(x) is differentiable, which of the following represents dydx\dfrac{dy}{dx}? (a) −sin⁡(g(x))-\sin\bigl(g(x)\bigr) (b) −sin⁡(g(x)) g′(x)-\sin\bigl(g(x)\bigr)\,g'(x) (c) sin⁡(g(x)) g′(x)\sin\bigl(g(x)\bigr)\,g'(x) (d) −sin⁡(g(x))g′(x)-\dfrac{\sin\bigl(g(x)\bigr)}{g'(x)}

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