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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 2 \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}

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

Simplify

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

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

\int \frac{1}{3 + x} d x

2 y^{^{'}} + 5 y = 4

\int cos (nπ \frac{x}{2}) d x

\frac{d}{d x} (6 + 5 f (x))

\int_{0.1}^{0.2} 600 x d x

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