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Suppose that the function f has derivatives of all orders at x and that F(x)=(mx+b)f(x)F(x)=(m x+b) f(x), where mm and bb are constants. Express F(x)F^{\prime \prime \prime}(x) in terms of x and derivatives of f.

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Answered 11 months ago
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In this exercise, we are tasked to find F(x)F'''(x) given that

F(x)=(mx+b)f(x),F(x)=(mx+b)f(x),

where:

mm and bb are constants,

f(x)f(x) has derivatives of all order at xx.

What differentiation rules should we use?

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