en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of tan^2(x/2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 tan (\frac{x}{2}) sec^{2} (\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 (2x-5^2)

\frac{d}{d x} ((2 x - 5)^{2})

integral from-6 to 6 of (2x+12)

\int_{- 6}^{6} (2 x + 12) d x

integral of (x^3)/(2x-1)

\int \frac{x ^{3}}{2 x - 1} d x

limit as x approaches 0 of |x|^x

x \to 0 lim (∣ x ∣^{x})

limit as x approaches 3-of 6/((x-3)^5)

x \to 3 - lim (\frac{6}{( x - 3 ) ^{5}})

Frequently Asked Questions (FAQ)

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