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  • Try this! - Limit , continuity and differentiability - JEE Main-10

Let f(x) = log _{e}\sin x  then f'(x) equals

  • Option 1)

    \sin x

  • Option 2)

    1/ \sin x

  • Option 3)

    \cot x

  • Option 4)

    \cos x

 

Answers (1)

best_answer

As we have learned

Logarithmic functions -

\frac{d}{dx}(log_{e}x)=\frac{1}{x}


\frac{d}{dx}(log_{e}f(x))=\frac{1}{f(x)}.\frac{d}{dx}f(x)

-

 

f'(x)=d(f(x))/dx= d(log _{e} \sin x)/dx=1/\sin x * d(\sin x)/dx= \cos x/\sin x= \cot x 

 

 

 

 

 


Option 1)

\sin x

Option 2)

1/ \sin x

Option 3)

\cot x

Option 4)

\cos x

Posted by

Himanshu

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