Answer:
[tex]\frac{d}{dt} [sec(\frac{t}{2} )] = \frac{1}{2} sec(\frac{t}{2} )tan(\frac{t}{2} )[/tex]
General Formulas and Concepts:
Calculus
- Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
- Trig u derivative: [tex]\frac{d}{dt} [sec(u)] = u'[sec(u)tan(u)][/tex]
Step-by-step explanation:
Step 1: Define
[tex]\frac{d}{dt} [sec(\frac{t}{2} )][/tex]
Step 2: Differentiate
- Trig u [Chain Rule/Basic Power]: [tex]\frac{d}{dt} [sec(\frac{t}{2} )] = \frac{t^{1-1}}{2} sec(\frac{t}{2} )tan(\frac{t}{2} )[/tex]
- Simplify: [tex]\frac{d}{dt} [sec(\frac{t}{2} )] = \frac{t^{0}}{2} sec(\frac{t}{2} )tan(\frac{t}{2} )[/tex]
- Evaluate: [tex]\frac{d}{dt} [sec(\frac{t}{2} )] = \frac{1}{2} sec(\frac{t}{2} )tan(\frac{t}{2} )[/tex]
