Question

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

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

For Daily Free Study Material Join wiredfaculty