en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of y=ln(sqrt(1-x^2))

Solution

derivative of

y = ln (1 - x^{2})

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral from 0 to y of 0.5

\int_{0}^{y} 0.5 d x

derivative of f(x)=cos(sqrt(sin(tan(pix))))

d er i v a t i v e f (x) = cos (sin (tan (π x)))

limit as x approaches 4 of ln|x-4|

x \to 4 lim (ln ∣ x - 4 ∣)

x^{3} + 3 y - x y^{^{'}} = 0

limit as x approaches pi/2 of tan^2(x)

x \to \frac{π}{2} lim (tan^{2} (x))

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(sqrt(1-x^2)) ?
The derivative of y=ln(sqrt(1-x^2)) is -x/(1-x^2)
What is the first derivative of y=ln(sqrt(1-x^2)) ?
The first derivative of y=ln(sqrt(1-x^2)) is -x/(1-x^2)