Explained: "Derivatives of logarithmic functions Calculate the derivative of..."

ossidianaZ

Answered question

2021-10-04

Derivatives of logarithmic functions Calculate the derivative of the following functions

y = \log_{8} | \tan x |

Anonym

Skilled2021-10-05Added 108 answers

Step 1
Given function is

y = \log_{8} | \tan x |

.
From Property of logarithm, we have

\log_{a} b = \frac{\ln b}{\ln a}

Therefore, given function can be written as:

y = \log_{8} | \tan x |

y = \frac{\ln | \tan x |}{\ln 8}

Step 2
We know that, the derivative of

\tan x = \sec^{2} x

.
Differentiating the given function with respect to x,

\frac{d y}{d x} = \frac{d}{d x} [\frac{\ln | \tan x |}{\ln 8}]

= \frac{1}{\ln 8} [\frac{1}{\tan x} \cdot \sec^{2} x]

= \frac{1}{\ln 8} [\frac{\sec^{2} x}{\tan x}]

Hence, the derivative of the given function is

\frac{1}{\ln 8} [\frac{\sec^{2} x}{\tan x}]

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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