Question

Find the derivative. It may be to your advantage to simplify before differentiating. Assume $a, b, c,$ and $k$ are constants. $$Q=a \ln (b x+c)$$

Name: Problem 8, Chapter 3: Calculus Single Variable
Uploaded: 2021-04-16T13:09:08-08:00
Duration: 35 s
Channel: Robert Daugherty
Description: Find the derivative. It may be to your advantage to simplify before differentiating. Assume a, b, c, and k are constants. Q=a ln(b x+c)

   Find the derivative. It may be to your advantage to simplify before differentiating. Assume $a, b, c,$ and $k$ are constants. $$Q=a \ln (b x+c)$$

Calculus Single Variable

Deborah… 7th Edition

Chapter 3, Problem 8

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Solved by Expert Robert Daugherty

04/16/2021

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Here, we have a function $Q=a \ln (b x+c)$ where $a, b, c,$ and $k$ are constants. Show more…

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Find the derivative. It may be to your advantage to simplify before differentiating. Assume $a, b, c,$ and $k$ are constants. $$Q=a \ln (b x+c)$$

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Key Concepts

Chain Rule

The chain rule is used to differentiate composite functions, meaning functions that can be represented as one function inside another. In the context of differentiating ln(bx + c), the chain rule allows us to take the derivative of the outer function (the natural logarithm) and multiply it by the derivative of the inner function (bx + c). This rule is essential for handling functions where variables are nested within other functions.

Derivative of Logarithm Function

When differentiating the natural logarithm function, recall that the derivative of ln(u) with respect to u is 1/u, provided u > 0. This fundamental concept is used to differentiate logarithmic expressions and forms the basis for further application of differentiation rules when the argument of the logarithm is a function of another variable.

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