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MATH_1225_17255_202501 3.6 Derivatives of Logarithmic Functions

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Assume y=f(x) and y=g(x) are non-constant functions. Let a and c  be constants. Select the appropriate derivative rule to be used for each. d dx (ca)  Constant Rule d dx (ag(x))  Exponential Rule d dx ((f(x))c)  Power Rule d dx ((f(x))g(x)) Logarithmic Differentiation

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Let's break down each derivative expression and identify the rule it calls for, keeping in mind which rules are actually listed. 1) d/dx (ca) where a and c are constants - This expression represents a constant, since the product of two constants is a constant. The derivative of any constant with respect to x is 0. Therefore, the appropriate rule here is the Constant Rule. - Why the other listed options don’t apply neatly: the Exponential Rule is used for derivatives involving exponential growth forms like e^{kx} or a^{x}, which this expression is not. The Power Rule applies to derivatives o......Login to view full explanation

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