Find the derivatives of the given functions. z(x)=\ln |\sec x+\tan x|

djeljenike

djeljenike

Answered question

2021-05-30

Find the derivatives of the given functions. z(x)=ln|secx+tanx|

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2021-05-31Added 104 answers

z(x)=ln|secx+tanx|
Differentiate both sides with respect to x
z(x)=ddx[ln|secx+tanx|]
Apply ddx[ln|u|]=1ududx
z(x)=1secx+tanxdxddx[secx+tanx]
Therefore,
z(x)=1secx+tanx(secxtanx+sec2x)
Simplify
z(x)=secxsecx+tanx(tanx+secx)
z(x)=secx

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