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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 1100 (x^{2} - 0.2 x)

3 x^{2} + 6, y = 6.4, y = 8.1

y = - 2 sin (x), at x = \frac{3}{4} π

\frac{d}{d x} (\frac{cos ( x )}{1 + cos ( x )})

n = 0 \sum \infty \frac{4 n}{- 4 n + 7}

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