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

In summary, Trigonometric integrals are integrals that involve trigonometric functions and are commonly used in solving problems in calculus and physics. They can be solved using techniques such as substitution, integration by parts, and trigonometric identities. Commonly used identities include Pythagorean identities, double angle identities, half angle identities, and power reducing identities. Trigonometric integrals can also be solved using software or calculators, with many graphing calculators and software programs available. These integrals have various applications in real life, including in fields such as physics, engineering, and mathematics, and are used to solve problems related to motion, vibrations, waves, and electrical circuits, as well as in calculating areas and volumes of irregular shapes
  • #1
bobsmith76
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Homework Statement



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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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  • #2
never mind. I got it. I've got to use the chain rule. the derivative of t/2 is 1/2
 

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

What are Trigonometric Integrals?

Trigonometric integrals are integrals in which the integrand contains trigonometric functions such as sine, cosine, tangent, etc. These integrals are used to solve problems in calculus and physics.

How do you solve Trigonometric Integrals?

To solve Trigonometric Integrals, you can use various techniques such as substitution, integration by parts, trigonometric identities, and partial fractions. It is important to identify the appropriate technique for each integral.

What are the common trigonometric identities used in solving Trigonometric Integrals?

The most commonly used trigonometric identities in solving Trigonometric Integrals are the Pythagorean identities, double angle identities, half angle identities, and power reducing identities. These identities help simplify the integrand and make it easier to integrate.

Can Trigonometric Integrals be solved using software or calculators?

Yes, Trigonometric Integrals can be solved using software or calculators. Many graphing calculators have built-in functions for evaluating Trigonometric Integrals. There are also various software programs, such as Mathematica and Wolfram Alpha, that can solve Trigonometric Integrals.

What are the applications of Trigonometric Integrals in real life?

Trigonometric Integrals have various applications in real life, especially in fields such as physics, engineering, and mathematics. They are used to solve problems related to motion, vibrations, waves, and electrical circuits. Trigonometric Integrals are also used in calculating areas and volumes of irregular shapes.

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