Find the derivatives of the functions defined as y=tan⁡xx−1

Step 1Consider the function: y=tan⁡xx−1.Find the derivative of y.Apply quotient rule of derivative that is (uv)′=vu′−v′uv2.Therefore,y′=(x−1)(tan⁡x)′−(x−1)′tan⁡x(x−1)2Step 2Use (tan⁡x)′=sec2x and (axn)=anxn−1Therefore,y′=(x−1)(sec2x)−tan⁡x(x−1)2

Expert answers to "Find the derivatives of the functions defined as..."

Khaleesi Herbert

Answered question

2021-10-19

Find the derivatives of the functions defined as

y = \frac{\tan x}{x - 1}

Answer & Explanation

Isma Jimenez

Skilled2021-10-20Added 84 answers

Step 1
Consider the function:

y = \frac{\tan x}{x - 1}

.
Find the derivative of y.
Apply quotient rule of derivative that is

{(\frac{u}{v})}^{'} = \frac{v u^{'} - v^{'} u}{v^{2}}

.
Therefore,

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

Step 2
Use

{(\tan x)}^{'} = \sec^{2} x and (a x^{n}) = a n x^{n - 1}

Therefore,

y^{'} = \frac{(x - 1) (\sec^{2} x) - \tan x}{{(x - 1)}^{2}}

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