Problem 102E

102. (a) If $F(x)=f(x) g(x)$, where $f$ and $g$ have derivatives of all orders, show that $F^{\prime \prime}=f^{\prime \prime} g+2 f^{\prime} g^{\prime}+f g^{\prime \prime}$

(b) Find similar formulas for $F^{w}$ and $F^{(9)}$.

(c) Guess a formula for $F^{(n)}$.

 

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