Derivatives of logarithmic functions Calculate the derivative of the following f

ossidianaZ 2021-10-04 Answered
Derivatives of logarithmic functions Calculate the derivative of the following functions
y=log8|tanx|
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Anonym
Answered 2021-10-05 Author has 108 answers
Step 1
Given function is y=log8|tanx|.
From Property of logarithm, we have
logab=lnblna
Therefore, given function can be written as:
y=log8|tanx|
y=ln|tanx|ln8
Step 2
We know that, the derivative of tanx=sec2x.
Differentiating the given function with respect to x,
dydx=ddx[ln|tanx|ln8]
=1ln8[1tanxsec2x]
=1ln8[sec2xtanx]
Hence, the derivative of the given function is 1ln8[sec2xtanx]
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