Question

Sec^2.x tan x. dx defferncsetaion

Answer 1

CORRECT QUESTION:

• Differentiate sec² x tan x

ANSWER:

• sec² x(sec² x +2 tan² x)

GIVEN:

• sec² x tan x

TO FIND:

• Derivative of sec² x tan x

EXPLANATION:

$\boxed{ \large{ \bold{ \frac{d}{dx} uv = uv' + vu'}}}$

d/dx(sec² x tan x) = sec²x d/dx(tan x) + tan x d/dx(sec²x)

$\boxed{ \huge{ \bold{ \frac{d}{dx} {x}^{2} =2x}}}$

$\boxed{ \huge{ \bold{ \frac{d}{dx} \tan x = \sec^{2} x}}}$

d/dx(sec² x tan x) = sec²x sec² x + tan x(2 sec x ) d/dx(sec x)

$\boxed{ \large{ \bold{ \frac{d}{dx} \sec x = \sec x \tan x}}}$

d/dx(sec² x tan x) = sec²x sec²x + 2 tan x sec x (sec x tan x)

d/dx(sec² x tan x) = sec⁴ x + 2 tan² x sec² x

d/dx(sec² x tan x) = sec² x(sec² x + 2 tan² x).