# If f(x)=tan−1(2cot2x1+cos2x) then ddx(f(f(x))) at x=π2 is

A

0

B

1

C

1

D

12

Text Solution
Verified by Experts

## f(x)=tan−1(2cot2x1+cos2x) =tan−1(2cos2x1−cos4x) =2tan−1(cos2x) f'(x)=−21+cos4x[2sinxcosx] f'(x)=4sinx.Cosx1+sin4x f'(π2)=0 ddxf(f(x))−f'(f(x))f'(x) ddxf(f(x)) at (x−π2)=f'(f(π2))f'(π2)=0.

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Updated on:21/07/2023

### Knowledge Check

• Question 1 - Select One

## If f(x)=tan−1(3x−x31−3x2) then ddx(f(x)) is equal to

A31+9x2 for all xR
B31+x2 for all xR
C31+x2 for all xR{13,13}
D19+x2
• Question 2 - Select One

## f(x)=sin−1(sinx) then ddxf(x) at x=7π2 is

A1
B1
CNot differentiable
DNone of these
• Question 3 - Select One

## if 2f ( sin x) + f( cos x) = x then ddxf(x) Is

A1(1x2)
Bsinx+cosx
C2
DNone

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