(All Steps) Without using the chain rule, prove the quotient rule of differentiation. That is, prove that if g(c) ≠q 0 then (f/g)^prime(c)=(f^prime(c)


Question: Without using the chain rule, prove the quotient rule of differentiation. That is, prove that if \(g(c) \neq 0\) then

\[\left(\frac{f}{g}\right)^{\prime}(c)=\frac{f^{\prime}(c) g(c)-f(c) g^{\prime}(c)}{g(c)^{2}}\]

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