Expert answers to "Find the derivatives of the given functions. s(x)=tan⁡xx2−1"

Lennie Carroll

Answered question

2021-06-04

Find the derivatives of the given functions.

s (x) = \frac{\tan x}{x^{2} - 1}

Tuthornt

Skilled2021-06-05Added 107 answers

s (x) = \frac{\tan x}{x^{2} - 1}

s (x) = \tan x \cdot {(x^{2} - 1)}^{- 1}

\frac{1}{x^{2} - 1}

{(x^{2} - 1)}^{- 1}

s^{'} (x) = \tan x \cdot \frac{d}{d x} ({(x^{2} - 1)}^{- 1}) + {(x^{2} - 1)}^{- 1} \cdot \frac{d}{d x} (\tan x) = \tan x \cdot (- 1) {(x^{2} - 1)}^{- 1 - 1} \cdot \frac{d}{d x} (x^{2} - 1) + {(x^{2} - 1)}^{- 1} \cdot \sec^{2} x = - \tan x {(x^{2} - 1)}^{- 2} \cdot 2 x + \frac{\sec^{2} x}{(x^{2} - 1)} = \frac{- 2 x \tan x}{{(x^{2} - 1)}^{2}} + \frac{\sec^{2} x}{x^{2} - 1}

Product rule

u = {(x^{2} - 1)}^{- 1}

u = x^{2} - 1

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