What is the derivative of arctan(7x) ?

The derivative of arctan(7x) is 7/(49x^2+1)

What is the first derivative of arctan(7x) ?

The first derivative of arctan(7x) is 7/(49x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

arctan (7 x)

\frac{7}{49 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (7 x))

Apply the chain rule:

\frac{1}{( 7 x ) ^{2} + 1} \frac{d}{d x} (7 x)

= \frac{1}{( 7 x ) ^{2} + 1} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= \frac{1}{( 7 x ) ^{2} + 1} \cdot 7

Simplify

\frac{1}{( 7 x ) ^{2} + 1} \cdot 7 : \frac{7}{49 x ^{2} + 1}

= \frac{7}{49 x ^{2} + 1}

What is the derivative of arctan(7x) ?
The derivative of arctan(7x) is 7/(49x^2+1)
What is the first derivative of arctan(7x) ?
The first derivative of arctan(7x) is 7/(49x^2+1)