Question

4. sin (ta1 e)

Answer 1

The function that is to be differentiated is,

sin( tan −1 e −x )

Differentiate the function.

d( sin( tan −1 e −x ) )=cos( tan −1 e −x )d( tan −1 e −x ) =cos( tan −1 e −x )× 1 1+ ( e −x ) 2 ×d( e −x ) =cos( tan −1 e −x )× − e −x dx 1+ ( e −x ) 2

Thus, the derivative of sin( tan −1 e −x )is d( sin( tan −1 e −x ) ) dx = − e −x cos( tan −1 e −x ) 1+ e −2x .