# A derivative formula a. Use the definition of the ## Problem 34E Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Problem 34E

A derivative formula a?. Use the definition of the derivative to determine d(?ax + b , where a ? ? and ?b dx are constants. d b.? Use the result of part (a) to find dx(?5x + 9 .

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SOLUTION STEP 1 (a). Here f(x) = ax + b We have to find df(x) = f(x) dx f(x+h)f(x) The definition of f(x) = lim h h0 Thus on substituting the given values into the definition,we get a(x+h)+b ax+b f(x) = lim h0 h To simplify this,we will multiply the numerator and the denominator with the conjugate of the numerator. Thus we get a(x+h)+b ax+b a(x+h)+b ax+b a(x+h)+b+ ax+b f(x) = lim h = lim h × h0 h0 a(x+h)+b+ ax+b 2 2 Here,using the formula...

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##### ISBN: 9780321570567

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A derivative formula a. Use the definition of the

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