Get the solution to "Find the derivatives of the functions y=2tan2x−sec2x" - Plainmath

kzae220o3

Answered question

2021-12-06

Find the derivatives of the functions

y = 2 \tan^{2} x - \sec^{2} x

Answer & Explanation

Louise Eldridge

Beginner2021-12-07Added 17 answers

Given,

y = 2 \tan^{2} x - \sec^{2} x

Step 2
Differentiating with respect to x, we get

\frac{d y}{d x} = \frac{d}{d x} (2 \tan^{2} x - \sec^{2} x)

= \frac{d (2 \tan^{2} x)}{d x} - \frac{d (\sec^{2} x)}{d x}

= 2 \cdot \frac{d (\tan^{2} x)}{d x} - \frac{d (\sec^{2} x)}{d x}

= 2 \cdot 2 \tan x \cdot \frac{d (\tan x)}{d x} - 2 \sec x \cdot \frac{d (\sec x)}{d x}

= 4 \tan x \cdot \sec^{2} x - 2 \sec x \cdot \sec x \tan x

= 2 \sec^{2} x (2 \tan x - \tan x)

= 2 \tan x \sec^{2} x

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