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What is the derivative of # f(x)=secx^2tan^2x#?

Answer 1

Isaiah Allen

#f' (x)=2*sec x^2*tan x*sec^2 x+2x*tan^2 x*sec x^2*tan x^2#

Using the specified function

#f(x)=sec x^2 tan^2 x#

#f' (x)=sec x^2*d/dx(tan^2 x)+tan^2 x * d/dx(sec x^2)#

#f' (x)=# #sec x^2*2*tan x*d/dx(tan x)+tan^2 x*sec x^2*tan x^2*d/dx(x^2)#

#f' (x)=2*sec x^2*tan x*sec^2 x+tan^2 x*sec x^2*tan x^2*2x#

#f' (x)=2*sec x^2*tan x*sec^2 x+2x*tan^2 x*sec x^2*tan x^2#

May God bless you all. I hope this explanation helps.

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Answer 2

Luke Alvarez

The derivative of ( f(x) = \sec^2(x)\tan^2(x) ) is ( f'(x) = 2\sec^2(x)\tan(x)\sec(x)\tan(x) + \sec^2(x)\tan^2(x)\sec^2(x) ), which simplifies to ( f'(x) = 2\sec^3(x)\tan^2(x) + \sec^4(x)\tan^2(x) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.