Math, asked by qarar, 1 year ago

F(x)=(Sec2x+tan2x)^2 FIND THE DERIVATIVE SHORTLY

Answers

Answered by GauravGumber

f(x)=(sec²x + tan²x)²=(1+tan²x+tan²x)²=(1+2tan²x)²
f'(x)=2*(1+2tan²x)* d(1+2tan ²x)/dx
=2*(1+2tan²x)*(0+2*2tanx*sec²x)
=2(1+2tan²x)(4tanx sec²x)
=8(1+2tan²x)(tanx sec²x)

qarar: PLZ HELP ME

GauravGumber: its okay

GauravGumber: how can i tell it just written above

GauravGumber: if you dont get leave this

kvnmurty: you have forgotten 2 before tan²x in line 3...

kvnmurty: can you modify ?

qarar: bro

GauravGumber: last step, 8sec²θ*sec²θ*tanθ=8sec⁴θ tanθ

GauravGumber: mark answer as brainliest , if you got it

GauravGumber: thanks kvnmurty to correct answer

Answered by kvnmurty

f(x) = (Sec 2x + Tan 2x)²

Derivative: we apply chain rule.

f '(x) = 2 * (Sec 2x + Tan 2x)²⁻¹ * d (Sec 2x + Tan 2x) / dx
= 2 (Sec 2x + Tan 2x) * (Sec 2x * Tan 2x * d(2x)/dx + Sec² 2x * d(2x)/dx )
= 2 (Sec 2x + Tan 2x) * Sec 2x ( Tan 2x * 2 + Sec 2x * 2)
= 4 Sec 2x * (Sec 2x + Tan 2x)²
= 4 Sec 2x (sec² 2x + tan² 2x + 2 sec 2x tan 2x)
= 4 Sec 2x (2 Sec² 2x + 2 sec 2x Tan 2x - 1)
= 8 sec³ 2x + 8 Sec² 2x Tan 2x - 4 sec 2x.

That is the answer.
The answer can be in many forms.. In the book one form may be given. But other forms are also right
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Rule:

Derivative of ( f(x) )ⁿ = n * ( f(x) )ⁿ⁻¹ * derivative of f(x).
Derivative of Tan 2x = Sec² 2x * derivative of 2x.

kvnmurty: :-) hope you can understand the detailed explanation.

kvnmurty: The answer can be in many forms.. In the book one form may be given. But other forms are also right.

qarar: wvbj

qarar: hello bro

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