Subjects calculus

Derivative Power A44B9C

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1. **Problem Statement:** Find the derivative $\frac{dy}{dx}$ of the function $y = x^{n-1}$, where $n$ is a natural number. 2. **Formula Used:** The power rule for differentiation states that if $y = x^m$, then $$\frac{dy}{dx} = m x^{m-1}$$ where $m$ is any real number. 3. **Apply the power rule:** Here, $m = n-1$. So, $$\frac{dy}{dx} = (n-1) x^{(n-1)-1} = (n-1) x^{n-2}$$ 4. **Explanation:** We subtract 1 from the exponent when differentiating, so the new exponent is $n-2$. 5. **Final answer:** $$\frac{dy}{dx} = (n-1) x^{n-2}$$ This corresponds to option B.