Why Does the Derivative of 2 + tan(x/2) Include a .5 Term?

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bobsmith76
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Homework Statement



Definite integral from -pi/2 to 0 of (2 + tan(t/2)) sec^2(t/2) dt, labeled 12a.


Handwritten-style worked solution of a substitution integral: u = 2 + tan(x/2), du = (1/2) sec^2(x/2) dx, then the limits are changed to u = 2 and u = 1 and the integral evaluates to 2^2 - 1^2 = 3.



I understand everything except why the derivative of 2 + tan (x/2) is .5 + sec^2(x/2)
I don't understand the .5 part. I understand the sec part. I would think the derivative of 2 would be C, or just disappear.
 
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never mind. I got it. I've got to use the chain rule. the derivative of t/2 is 1/2
 

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