What is the derivative of 4sec(x/2) ?

The derivative of 4sec(x/2) is 2sec(x/2)tan(x/2)

What is the first derivative of 4sec(x/2) ?

The first derivative of 4sec(x/2) is 2sec(x/2)tan(x/2)

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\frac{d}{d x} (4 sec (\frac{x}{2}))

2 sec (\frac{x}{2}) tan (\frac{x}{2})

Solution steps

\frac{d}{d x} (4 sec (\frac{x}{2}))

Take the constant out:

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

= 4 \frac{d}{d x} (sec (\frac{x}{2}))

Apply the chain rule:

sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{d}{d x} (\frac{x}{2})

= sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{d}{d x} (\frac{x}{2})

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

= 4 sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2}

Simplify

4 sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2} : 2 sec (\frac{x}{2}) tan (\frac{x}{2})

= 2 sec (\frac{x}{2}) tan (\frac{x}{2})

\int sec^{2} (x) - 8 cot (x) d x

y^{^{''}} + 36 y = 24 sin (6 t)

y = \frac{1}{7 t ^{3}}

x \to 1 + lim ((1 - x)^{l n (x)})

\int_{2}^{3} \frac{38}{3 - x} d x

What is the derivative of 4sec(x/2) ?
The derivative of 4sec(x/2) is 2sec(x/2)tan(x/2)
What is the first derivative of 4sec(x/2) ?
The first derivative of 4sec(x/2) is 2sec(x/2)tan(x/2)