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  • Solve this problem - Limit , continuity and differentiability - JEE Main-12

Let f(x) =\csc (x^{2}) then f'(x) equals

  • Option 1)

    -\csc(x^{2})\cot (x^{2})

  • Option 2)

    \csc(x^{2})\cot (x^{2})

  • Option 3)

    -2x\csc(x^{2})\cot (x^{2})

  • Option 4)

    2x\csc(x^{2})\cot (x^{2})

 

Answers (1)

best_answer

As we have learned 

 

Trigonometric functions -

\frac{d}{dx}(sinx)=cosx

\frac{d}{dx}(secx)=secx\:tanx

\frac{d}{dx}(cosec\:f(x))=-cosec\:\left \{ f(x) \right \}\:cot\:\left \{ f(x) \right \}\;f'(x)

-

 

 

 f'(x)= \frac{d}{dx}\csc x^{2} = -\csc x^{2} \cot x^{2} \frac{d}{dx}x^{2} = -2 x\csc x^{2}\cot x^{2}

 

 

 

 

 


Option 1)

-\csc(x^{2})\cot (x^{2})

Option 2)

\csc(x^{2})\cot (x^{2})

Option 3)

-2x\csc(x^{2})\cot (x^{2})

Option 4)

2x\csc(x^{2})\cot (x^{2})

Posted by

Himanshu

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