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Question

4. sin (ta1 e)

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Solution

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 .


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