What is the derivative of (2tan(x)/(1-tan^2(x))) ?

The derivative of (2tan(x)/(1-tan^2(x))) is sec^2(2x)*2

What is the first derivative of (2tan(x)/(1-tan^2(x))) ?

The first derivative of (2tan(x)/(1-tan^2(x))) is sec^2(2x)*2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

sec^{2} (2 x) \cdot 2

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

= sec^{2} (2 x) \cdot 2

What is the derivative of (2tan(x)/(1-tan^2(x))) ?
The derivative of (2tan(x)/(1-tan^2(x))) is sec^2(2x)*2
What is the first derivative of (2tan(x)/(1-tan^2(x))) ?
The first derivative of (2tan(x)/(1-tan^2(x))) is sec^2(2x)*2