Please solve the following proof discrete math **B.** Use the product rule and induction (but NOT the chain rule) to prove that if \( f(x) \) is a differentiable function, then for any \( n \geq 1 \),\[\frac{d}{dx}(f(x))^n = n(f(x))^{n-1} \cdot f'(x).\]

Answered: B. Use the product rule and induction…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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B. Use the product rule and induction (but NOT the chain rule) to prove that if f(x) is a differ- entiable function, then for any n ≥ 1, -(ƒ(x))" = n(ƒ(x))"-¹. f'(x). dx