en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arctan(sqrt(x-1))

Solution

\frac{d}{d x} (arctan (x - 1))

Solution

\frac{1}{2 x x - 1}

Solution steps

\frac{d}{d x} (arctan (x - 1))

Apply the chain rule:

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

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

\frac{d}{d x} (x - 1) = \frac{1}{2 x - 1}

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

Simplify

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

= \frac{1}{2 x x - 1}

Popular Examples

derivative of 5/(sqrt(e^x+x))

\frac{d}{d x} (\frac{5}{e ^{x} + x})

limit as x approaches 1+of (x-3)^2

x \to 1 + lim ((x - 3)^{2})

y^{''}-4y^'+29y=0

y^{^{''}} - 4 y^{^{'}} + 29 y = 0

derivative of (2e^x-x^5/(1-3x^5))

\frac{d}{d x} (\frac{2 e ^{x} - x ^{5}}{1 - 3 x ^{5}})

derivative of xe^{xy+1}

\frac{d}{d x} (x e^{x y + 1})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(sqrt(x-1)) ?
The derivative of arctan(sqrt(x-1)) is 1/(2xsqrt(x-1))
What is the first derivative of arctan(sqrt(x-1)) ?
The first derivative of arctan(sqrt(x-1)) is 1/(2xsqrt(x-1))