Sponsor Area

Continuity And Differentiability

Question
CBSEENMA12035350

If space straight x equals log space straight theta comma space straight theta greater than 0 space and space straight y equals 1 over straight theta space then space show space that space fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx equals 0.

Solution
space space space space space space space space space space space straight x equals log space straight theta comma space space space straight y equals 1 over straight theta
therefore space dx over dθ equals 1 over straight theta comma space dy over dθ equals negative 1 over straight theta squared
space space space space space space dy over dx equals fraction numerator begin display style dy over dθ end style over denominator begin display style dx over dθ end style end fraction equals negative 1 over straight theta squared cross times straight theta over 1 equals negative 1 over straight theta equals negative straight theta to the power of negative 1 end exponent
therefore space fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative left parenthesis negative 1 right parenthesis straight theta to the power of negative 2 end exponent dθ over dx equals 1 over straight theta squared. straight theta equals 1 over straight theta
space space space space straight L. straight H. straight S equals fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx equals 1 over straight theta minus 1 over straight theta equals 0
space space space space space space space space space space space space space space space equals straight R. straight H. straight S.

Some More Questions From Continuity and Differentiability Chapter