How do you find the derivative of # ln|x|#?
The derivative of lnx is a fundamental calculus result.
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To find the derivative of ln|x|, where ln denotes the natural logarithm and |x| represents the absolute value of x, you apply the chain rule. The derivative is:
d/dx ln|x| = (1/x) * (d/dx |x|) = (1/x) * (d/dx x)
Now, differentiate |x|, considering x as a piecewise function:
For x > 0: |x| = x For x < 0: |x| = -x
So, d/dx |x| = 1 for x > 0 and -1 for x < 0.
Thus, d/dx ln|x| = 1/x for x > 0 and -1/x for x < 0.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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