We have an answer to "Find the derivatives of the functions y=ln⁡(sec⁡2θ)" - Plainmath

Caelan

Answered question

2021-10-15

Find the derivatives of the functions

y = \ln (\sec 2 θ)

Answer & Explanation

Neelam Wainwright

Skilled2021-10-16Added 102 answers

Step 1
Given:

y = \ln (\sec 2 θ)

For finding derivative of given function we use property of differentiation

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

and

\frac{d}{d x} (\sec x) = \sec x \tan x

Step 2
So,

\frac{d}{d x} (\ln (\sec 2 θ)) = \frac{1}{\sec (2 θ)} \cdot \sec (2 θ) \tan (2 θ) \cdot 2

\frac{d}{d x} (\ln (\sec 2 θ)) = \frac{2 \sec (2 θ) \tan (2 θ)}{\sec (2 θ)}

\frac{d}{d x} (\ln (\sec (2 θ)) = 2 \tan (2 θ)

Hence, given differentiation is

2 \tan (2 θ)

.

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