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To differentiate y = a^(cos x) with respect to x, we use the chain rule.The derivative of a^u with respect to u is a^u ln a.Here, u = cos x, so dy/du = a^(cos x) ln a.The derivative of u with respect to x is du/dx = d/dx (cos x) = -sin x.By the chain rule, dy/dx = (dy/du) * (du/dx) = (a^(cos x) ln a) * (-sin x) = -sin x a^(cos x) ln a.