What is the derivative of sec^3(x/2) ?

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

What is the first derivative of sec^3(x/2) ?

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

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derivative of

sec^{3} (\frac{x}{2})

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

Solution steps

\frac{d}{d x} (sec^{3} (\frac{x}{2}))

Apply the chain rule:

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

= 3 (sec (\frac{x}{2}))^{2} \frac{d}{d x} (sec (\frac{x}{2}))

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

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

Simplify

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

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

\frac{1}{( 2 x + 2 )}

lo g_{10} (x^{6} + 5)

y = (x + a)^{3}

cot^{\frac{1}{2}} (x)

(4 - x^{2})^{2}

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