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Find the second derivative of natural log x

User Da Tong
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Final answer:

The second derivative of the natural logarithm of x, ln(x), is found by first determining the first derivative, which is 1/x, and then differentiating again to get -1/x^2.

Step-by-step explanation:

To find the second derivative of the natural logarithm of x, ln(x), we first need to know the first derivative. The first derivative of ln(x) is 1/x, as it's a well-known result of differentiation. Applying the derivative operation again to find the second derivative, we will differentiate 1/x.

The derivative of 1/x with respect to x is -1/x^2. This negative comes from the rule that the derivative of x-1 (which is another way to write 1/x) is -1 times x to the power of negative two.

Therefore, the second derivative of the natural logarithm of x, ln(x), is -1/x^2.

User Thomas Ward
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