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  • Solve! - Limit , continuity and differentiability - JEE Main-13

Which of the following function don't have derivative zero for all x \epsilon (-\pi /2,\pi /2)  ?

  • Option 1)

    \sin^{2}x+ \cos^{2}x

  • Option 2)

    \sec^{2}x+ \tan^{2}x

  • Option 3)

    \cos 2x - \cos^{2} x + \sin^{2} x

  • Option 4)

    x/x

 

Answers (1)

best_answer

As we have learned

Rule for differentiation -

The derivative of a constant function is zero.

- wherein

\therefore \:\:\:\frac{d}{dx}(c)=0

 

 (A),( B), and ( C)  are 1,1 and 0 respectively for all x\epsilon (-\pi /2,\pi /2) so they are constant in (-\pi /2,\pi /2) so have derivative zero in entire interval 

But (D) , x/x

 is one except at x= 0 so it is not constant for all  x\epsilon (-\pi /2,\pi /2) so its derivative is not always zero in  (-\pi /2,\pi /2)

 

 

 

 

 


Option 1)

\sin^{2}x+ \cos^{2}x

Option 2)

\sec^{2}x+ \tan^{2}x

Option 3)

\cos 2x - \cos^{2} x + \sin^{2} x

Option 4)

x/x

Posted by

Himanshu

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