Wednesday, January 6, 2016

calculus - Differentiate $:textrm{ln}sqrt{textrm{ln}:x}$

I am confused about the solution and method of differentiating this function:



$$\frac{d}{dx}\:\textrm{ln}\sqrt{\textrm{ln}\:x}$$



Why is ln not considered a constant and then multiplied by the derivative of$\:\sqrt{\textrm{ln}\:x}$ ?




The solution is given as:



$$\left(\frac{1}{2x\:\textrm{ln}x}\right)$$
How exactly is the chain rule applied to the entire function at once?

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