Question
Given that $(a+b)^{4}=a^{4}+4 a^{3} b+6 a^{2} b^{2}+4 a b^{3}+b^{4},$ write out a formula for $F^{(4)}(x)$. (See exercise 41 .)
Step 1
We can use this formula to derive the fourth derivative of a product of two functions, $F(x) = f(x)g(x)$. Show more…
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Key Concepts
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With $F(x)$ defined as in exercise $45,$ compute $F^{(4)}(x)$ using the fact that $(a+b)^{4}=a^{4}+4 a^{3} b+6 a^{2} b^{2}+4 a b^{3}+b^{4}$.
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