Differentiate the following functions with respect to x -x tan x- x-tan x

We have, d/dx(x tan x/sec x+tan x ) Using quotient rule, we get =(sec x+tan x)d/dx(x tan x) (x tan x)d/dx(sec x+tan x)/(sec x+tan x)^2 =(sec x+tan x)(x sec^2x+t ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Quotient Rule of Differentiation

Differentiate...

Question

Differentiate the following functions with respect to x :

$\frac{x t a n x}{s e c x + t a n x}$

Open in App

Solution

We have,

$\frac{d}{d x} (\frac{x t a n x}{s e c x + t a n x})$

Using quotient rule, we get

$= \frac{(s e c x + t a n x) \frac{d}{d x} (x t a n x) - (x t a n x) \frac{d}{d x} (s e c x + t a n x)}{(s e c x + t a n x)^{2}}$ $= \frac{(s e c x + t a n x) (x s e c^{2} x + t a n x) - (x t a n x) (s e c x t a n x + s e c^{2} x)}{(s e c x + t a n x)^{2}}$ [Using product rule]

$= \frac{(s e c x + t a n x) (x s e c^{2} x + t a n x) - x s e c x + t a n^{2} x - x t a n x s e c^{2} x}{(s e c x + t a n x)^{2}}$

$= \frac{(s e c x + t a n x) (x s e c^{2} x + t a n x) - x t a n x (s e c x t a n x + s e c^{2} x)}{(s e c x + t a n x)^{2}}$

$= \frac{(s e c x + t a n x) (x s e c^{2} x + t a n x) - x t a n x s e c x (s e c x + t a n x)}{(s e c x + t a n x)^{2}}$

$= \frac{(s e c^{2} x + t a n x - x t a n x s e c x) (s e c x + t a n x)}{(s e c x + t a n x)^{2}}$

$= \frac{(x s e c^{2} + t a n x - x t a n x s e c x)}{s e c x + t a n x} = \frac{x s e c (s e c x - t a n x) + t a n x}{(s e c x + t a n x)}$

Suggest Corrections

Similar questions

Differentiate the following functions with respect to x :

$\frac{e^{x} - t a n x}{c o t x - x^{n}}$

Differentiate the following functions with respect to x :

$\frac{x}{1 + t a n x}$

Differentiate the following functions with respect to x :

$\frac{3^{x}}{x + t a n x}$

Q. Differential the following functions w.e.t.x:

\frac{x tan x}{sec x + tan x}

Differentiate the following functions with respect to x :

$\frac{x + c o s x}{t a n x}$

Join BYJU'S Learning Program

Differentiate the following functions with respect to x : x tan xsec x+tan x

Differentiate the following functions with respect to x :

$\frac{x t a n x}{s e c x + t a n x}$