Find out the answer to "Find the derivative of the following functions y=ln⁡(ln⁡x)" - Plainmath

Tammy Todd

Answered question

2021-10-10

Find the derivative of the following functions

y = \ln (\ln x)

Answer & Explanation

Raheem Donnelly

Skilled2021-10-11Added 75 answers

Step 1
Given:

y = \ln (\ln x)

Step 2
Solution:
Derivative both sides with respect to x

\frac{d}{d x} (y) = \frac{d}{d x} [\ln (\ln x)]

\frac{d y}{d x} = \frac{1}{\ln x} \frac{d}{d x} (\ln x) \Rightarrow [\frac{d}{d x} (\ln (x)) = \frac{1}{x} (\frac{d}{d x} x)]

\frac{d y}{d x} = \frac{1}{\ln x} (\frac{1}{x})

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

Step 3
Answer:

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

Jeffrey Jordon

Expert2022-03-24Added 2605 answers

Answer is given below (on video)

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