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Popular >

derivative of sec^2(x/2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

= 2 sec (\frac{x}{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}

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

Simplify

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

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

Popular Examples

derivative of (2-x^2/(3x^2+1))

\frac{d}{d x} (\frac{2 - x ^{2}}{3 x ^{2} + 1})

limit as x approaches-1+of (x^2+x)/(x+1)

x \to - 1 + lim (\frac{x ^{2} + x}{x + 1})

derivative of x^2*x^7

\frac{d}{d x} (x^{2} \cdot x^{7})

(\partial)/(\partial y)(x^4y^2-x^3y)

\frac{\partial}{\partial y} (x^{4} y^{2} - x^{3} y)

derivative of 2x^3+1

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

Frequently Asked Questions (FAQ)

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