Prove the product rule. Hint: Use f(x)g(x) - f(c)g(c) = f(x)(g(x) - g(c)) + g(c)(f(x) - f(c)).
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We want to prove the product rule, which states that if we have two functions $f(x)$ and $g(x)$, then the derivative of their product is given by: $$(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)$$ We are given the hint to use the following equation: $$f(x)g(x) - f(c)g(c) Show more…
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