What is the derivative of $\frac{tan x}{sin x}$ $tanx/sinx$ ?

Question

What is the derivative of $\frac{tan x}{sin x}$ $tanx/sinx$ ?

2 Answers

Impact of this question

9637 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-03T18:11:38

$\frac{d}{d x} {\frac{tan x}{sin x}} = \frac{d}{d x} {\frac{sin x}{cos x} \cdot \frac{1}{sin x}} = \frac{d}{d x} {\frac{1}{cos x}}$ $d/dx{tanx/sinx}=d/dx{sinx/cosx*1/sinx}=d/dx{1/cosx}$
$= \frac{d}{d x} {sec x} = sec x tan x$ $=d/dx{secx}=secxtanx$ .

Answer 2 · 2018-05-04T12:49:06

$sec x tan x$ $secxtanx$

Explanation:

Given: $\frac{d}{d x} (\frac{tan x}{sin x})$ $d/dx(tanx/sinx)$ .

Notice how $tan x = \frac{sin x}{cos x}$ $tanx=sinx/cosx$ .

$= \frac{d}{d x} (\frac{sin x}{cos x} \cdot \frac{1}{sin x})$ $=d/dx(sinx/cosx*1/sinx)$

$= \frac{d}{d x} (\frac{1}{cos x})$ $=d/dx(1/cosx)$

Now, we know that $\frac{1}{cos x} = sec x$ $1/cosx=secx$ .

$= \frac{d}{d x} (sec x)$ $=d/dx(secx)$

This is a well known integral, where it equals,

$= sec x tan x$ $=secxtanx$

Science

Math

Humanities

... and beyond

What is the derivative of $\frac{tan x}{sin x}$ $tanx/sinx$ ?

2 Answers

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the derivative of tanxsinxtanx/sinx?

2 Answers

Explanation:

Related questions

Impact of this question

What is the derivative of $\frac{tan x}{sin x}$ $tanx/sinx$ ?