What is the derivative of 2cos^2(t/2) ?

The derivative of 2cos^2(t/2) is -sin(t)

What is the first derivative of 2cos^2(t/2) ?

The first derivative of 2cos^2(t/2) is -sin(t)

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derivative of

2 cos^{2} (\frac{t}{2})

- sin (t)

Solution steps

\frac{d}{d t} (2 cos^{2} (\frac{t}{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d t} (cos^{2} (\frac{t}{2}))

Apply the chain rule:

2 cos (\frac{t}{2}) \frac{d}{d t} (cos (\frac{t}{2}))

= 2 cos (\frac{t}{2}) \frac{d}{d t} (cos (\frac{t}{2}))

\frac{d}{d t} (cos (\frac{t}{2})) = - sin (\frac{t}{2}) \frac{1}{2}

= 2 \cdot 2 cos (\frac{t}{2}) (- sin (\frac{t}{2}) \frac{1}{2})

Simplify

2 \cdot 2 cos (\frac{t}{2}) (- sin (\frac{t}{2}) \frac{1}{2}) : - sin (t)

= - sin (t)

What is the derivative of 2cos^2(t/2) ?
The derivative of 2cos^2(t/2) is -sin(t)
What is the first derivative of 2cos^2(t/2) ?
The first derivative of 2cos^2(t/2) is -sin(t)