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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

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

Advanced Engineering Mathematics
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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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 \( n \geq 1 \), \[ \frac{d}{dx}(f(x))^n = n(f(x))^{n-1} \cdot f'(x). \]
Transcribed Image Text:**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 \( n \geq 1 \), \[ \frac{d}{dx}(f(x))^n = n(f(x))^{n-1} \cdot f'(x). \]
Expert Solution
Step 1: Product Rule

We use the product rule and then solve this problem. 

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