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Popular >

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}}

Popular Examples

integral from 0 to y of 0.5

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

derivative of sqrt(4-x^2)derivative of

4 - x^{2}

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

f (x) = cos (sin (tan (π x)))

(dy}{dx}= 1/x y-\frac{x^2)/3 y^4

\frac{d y}{d x} = \frac{1}{x} y - \frac{x ^{2}}{3} y^{4}

tangent of y=(2x)/(1+x^2),(4, 8/17)tangent of

y = \frac{2 x}{1 + x ^{2}}, (4, \frac{8}{17})

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)