Question

derivative of ln*lnx?​

Answer 1

Step-by-step explanation:

First of all, inorder to solve this question, we need to understand chain rule. Chain rule is useful to differentiate some composite function.

Let's say we have a function f(g(x)), the derivative of this function is given by f'(g(x))*g'(x). We will use this concept to solve our problem.

Solution:

Consider,

$\sf\implies f(x) = \ln(\ln(x))$

Differentiating both sides w.r.t. x we get:

$\sf\implies f'(x) = \dfrac{d}{dx}( \ln(\ln(x)) )$

We know that:

• $\boxed{\frac{d}{dx} (\ln(x)) = \frac1 x}$

$\sf\implies f'(x) = \dfrac{1}{ \ln(x)} \times \dfrac{d}{dx}\ln(x)$

$\sf\implies f'(x) = \dfrac{1}{ \ln(x)} \times \dfrac{1}{x}$

$\sf\implies \underline{ \underline{f'(x) = \dfrac{1}{x \ln(x)} }}$

This is the required answer.

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