Question

$Differentiate space the space following space straight w. straight r. straight t. straight x colon space left parenthesis sin space straight x right parenthesis to the power of cos to the power of negative 1 end exponent straight x end exponent$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

space space space space space Let space straight y equals left parenthesis sin space straight x right parenthesis to the power of cos to the power of negative 1 end exponent straight x end exponent therefore space log space straight y equals log left parenthesis sin space straight x right parenthesis to the power of cos to the power of negative 1 end exponent straight x end exponent equals cos to the power of negative 1 end exponent straight x. space log space sin space straight x therefore space 1 over straight y dy over dx equals left parenthesis cos to the power of negative 1 end exponent straight x right parenthesis. fraction numerator cos space straight x over denominator sin space straight x end fraction minus fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction. log space sin space straight x therefore space dy over dx equals open parentheses sin space straight x close parentheses to the power of cos to the power of negative 1 end exponent straight x end exponent open square brackets cot space straight x. space cos to the power of negative 1 end exponent straight x minus fraction numerator log space sin space straight x over denominator square root of 1 minus straight x squared end root end fraction close square brackets

For Daily Free Study Material Join wiredfaculty