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

The derivative of (x^2-1^{1/2}) is x/((x^2-1)^{1/2)}

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

The first derivative of (x^2-1^{1/2}) is x/((x^2-1)^{1/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\int e^{z + e^{z}} d z

\frac{d}{d x} (e^{15 x})

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

x^{4} + 2 x

What is the derivative of (x^2-1^{1/2}) ?
The derivative of (x^2-1^{1/2}) is x/((x^2-1)^{1/2)}
What is the first derivative of (x^2-1^{1/2}) ?
The first derivative of (x^2-1^{1/2}) is x/((x^2-1)^{1/2)}