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

Thread starter bobsmith76
Start date Feb 3, 2012
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Integrals Trigonometric

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The derivative of the function 2 + tan(x/2) is .5 + sec^2(x/2) due to the application of the chain rule. The constant term 2 contributes a derivative of 0, while the derivative of tan(x/2) requires the chain rule, resulting in the .5 factor. The derivative of x/2 is 1/2, which is why this term appears in the final result. Understanding the chain rule is crucial for correctly calculating derivatives of composite functions. The discussion highlights the importance of recognizing how derivatives of inner functions affect the overall derivative.

Feb 3, 2012

bobsmith76

Homework Statement

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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Feb 3, 2012

bobsmith76

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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