Derivative of ln x to power of x Using Logarithms

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There is a way you can do that without using log differentiation. You change (ln(x))^x to base e as e^(xln(ln(x))). Then differentiate here. You get e^(xln(ln(x)))(ln(ln(x))+1/ln(x)), or

justabunga
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Could you make a video explaining why does the ln function is used to calculate decreasing quantities such as the radioative decay formula or the chemical kinetics' formula for changin in concentration with time [The radioactive decay formula,
ln(N0/N) = kt and ln[A]t-ln[A]0 = -kt is the concentration formula.

marcello
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Sir please also tell me the derivative of root x Power root x

mukhtiarsingh
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Sir g Plz Jaldi jakdi bataya karain itna time nai hota

ahmaraleem