If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)

If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)

Answer Details

To find \(\frac{dy}{dx}\), we need to differentiate y with respect to x using the chain rule and the power rule of differentiation. Using the chain rule, we get: \(\frac{dy}{dx}\) = \(\frac{d}{dx}\)(5 - x)\(^{-3}\) = -3(5 - x)\(^{-4}\)\(\frac{d}{dx}\)(5 - x) = -3(5 - x)\(^{-4}\)(-1) = \(\frac{3}{(5 - x)^4}\) Therefore, the correct answer is (c) \(\frac{3}{(5 - x)^4}\).