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Find the derivatives of the given functions.$$y=\ln (\ln x)$$

$\frac{d y}{d x}=\frac{1}{x \ln x}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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mhm. We want to define the derivative. Dy DX four. Why is equal to the natural algorithm of the algorithm events just solve this problem. We need to rely on differentiation shortcuts. We picked up through a single variable calculus in particular those related to algorithmic functions. So I've noted relevant rules here on the left. Rule zero is derivative rules for taking log B U D X and dx. Ellen you on the right? I noted. 123 respectively the power rule, product rule in chain rule. Mhm. Why is already in its most easily defensible form? So we see that we have to use rule zero along with the channel to solve. So let's proceed to the derivative. D D X L N U equals one over you. D you D X. Where for this problem you is itself L N X. Do I D x S one over LNX Times du DX which is one of the exits the river. LNX is just one over X. Thus we have final solution. Dy dx equals one over XLNX as his box on the right

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