+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Continuity And Differentiability

Question
CBSEENMA12035042
Wired Faculty App

Differentiate xsin xw.r.t. (sin x)x

Solution
Let space space space space space space straight y equals straight x to the power of sin space straight x end exponent comma space straight u equals left parenthesis sin space straight x right parenthesis to the power of straight x therefore space log space straight y equals log space straight x to the power of sin space straight x end exponent equals sin space straight x. log space straight x space rightwards double arrow space 1 over straight y dy over dx equals sin space straight x.1 over straight x plus log space straight x. cos space straight x therefore space space dy over dx equals space straight x to the power of sin space straight x end exponent open square brackets fraction numerator sin space straight x over denominator straight x end fraction plus cos space straight x. log space straight x close square brackets Also space space space straight u equals left parenthesis sin space straight x right parenthesis to the power of straight x therefore space log space straight u equals log left parenthesis sin space straight x right parenthesis to the power of straight x equals straight x. log left parenthesis sin space straight x right parenthesis therefore space 1 over straight u du over dx equals straight x. straight d over dx left square bracket log left parenthesis sin space straight x right parenthesis right square bracket plus log left parenthesis sin space straight x right parenthesis. straight d over dx left parenthesis straight x right parenthesis therefore space du over dx equals straight u open square brackets straight x.1 over sinx. cos space straight x plus log left parenthesis sin space straight x right parenthesis.1 close square brackets therefore space du over dx equals left parenthesis sin space straight x right parenthesis to the power of straight x left square bracket straight x space cot space straight x plus log left parenthesis sin space straight x right parenthesis right square bracket Now space dy over du equals fraction numerator begin display style dy over dx end style over denominator begin display style du over dx end style end fraction equals fraction numerator straight x to the power of sin space straight x end exponent open square brackets begin display style fraction numerator sin space straight x over denominator straight x end fraction end style plus cos space straight x. log space straight x close square brackets over denominator left parenthesis sin space straight x right parenthesis to the power of straight x left square bracket straight x space cot space straight x plus log left parenthesis sin space straight x right parenthesis right square bracket end fraction

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation