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Explain how the formula for differentiating the natural logarithm function is a special case of the formula for differentiating logarithmic functions of the formlogbx

Short Answer

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Step by step solution

01

Step 1. Given information

We have to explain how the formula for differentiating the natural logarithm function is a special case of the formula for differentiating logarithmic functions of the formlogbx.

02

Step 2. Explanation

For any constant b>0 with b1 and all approximate values of x,

ddxlogbx=1xlnb,ddxlnx=1x,ddxln|x|=1x

The second rule is a special case of the first with b = e. Because In x has domain (0,) when we say that ddxlnx=1xwe are also restricting 1xto the domain (0,).

In the third rule we consider the full domain as (-,0)(0,).

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