Question

Differentiate the following w.r.t.x: $tan to the power of negative 1 end exponent open square brackets open parentheses fraction numerator 1 minus cos space straight x over denominator 1 plus cos space straight x end fraction close parentheses to the power of 1 half end exponent close square brackets$

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

Solution

Let space straight y equals tan to the power of negative 1 end exponent open square brackets open parentheses fraction numerator 1 minus cos space straight x over denominator 1 plus cos space straight x end fraction close parentheses to the power of 1 half end exponent close square brackets comma space space space space therefore space straight y equals tan to the power of negative 1 end exponent open square brackets open parentheses fraction numerator 2 sin squared begin display style straight x over 2 end style over denominator 2 cos squared straight x over 2 end fraction close parentheses to the power of 1 half end exponent close square brackets rightwards double arrow space space straight y equals tan to the power of negative 1 end exponent open square brackets open parentheses fraction numerator sin begin display style straight x over 2 end style over denominator cos straight x over 2 end fraction close parentheses close square brackets space space space space rightwards double arrow space straight y equals tan to the power of negative 1 end exponent open parentheses tan straight x over 2 close parentheses rightwards double arrow space space straight y equals straight x over 2 comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space therefore space dy over dx equals 1 half

For Daily Free Study Material Join wiredfaculty