What is the derivative of ln raised to a power?

Question

For example: ln⁵

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Answer 1

If we have a function of x raised to a power, we use the chain rule:

d/dx (ln(x))^5 = 5(lnx)^4 * d/dx ln(x) = 5(lnx)^4 * 1/x = (5/x)*(lnx)^4.