What is the derivative of sec(1/2 xtan(1/2 x)) ?

The derivative of sec(1/2 xtan(1/2 x)) is 1/2 tan^2(x/2)sec(x/2)+1/2 sec^3(x/2)

What is the first derivative of sec(1/2 xtan(1/2 x)) ?

The first derivative of sec(1/2 xtan(1/2 x)) is 1/2 tan^2(x/2)sec(x/2)+1/2 sec^3(x/2)

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

\frac{1}{2} tan^{2} (\frac{x}{2}) sec (\frac{x}{2}) + \frac{1}{2} sec^{3} (\frac{x}{2})

Solution steps

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

Simplify

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (\frac{x}{2}), g = tan (\frac{x}{2})

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

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

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

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

Simplify

sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2} tan (\frac{x}{2}) + sec^{2} (\frac{x}{2}) \frac{1}{2} sec (\frac{x}{2}) : \frac{1}{2} tan^{2} (\frac{x}{2}) sec (\frac{x}{2}) + \frac{1}{2} sec^{3} (\frac{x}{2})

= \frac{1}{2} tan^{2} (\frac{x}{2}) sec (\frac{x}{2}) + \frac{1}{2} sec^{3} (\frac{x}{2})

\frac{d}{d x} (\frac{a}{x ^{2} + b})

y = x^{8}

\frac{d}{d y} (x^{2} + 2 x y + y^{2})

\int x cos (\frac{nπ x}{l}) d x

\int (4 x + 2) ln (x + 1) d x

What is the derivative of sec(1/2 xtan(1/2 x)) ?
The derivative of sec(1/2 xtan(1/2 x)) is 1/2 tan^2(x/2)sec(x/2)+1/2 sec^3(x/2)
What is the first derivative of sec(1/2 xtan(1/2 x)) ?
The first derivative of sec(1/2 xtan(1/2 x)) is 1/2 tan^2(x/2)sec(x/2)+1/2 sec^3(x/2)