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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (x^2-25/(x+5))

\frac{d}{d x} (\frac{x ^{2} - 25}{x + 5})

derivative of x^4+4/3 x^3-4x^2

\frac{d}{d x} (x^{4} + \frac{4}{3} x^{3} - 4 x^{2})

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

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x \to 0 lim (\frac{7 e ^{x}}{x ^{5}})

integral of 4x^2-2

\int 4 x^{2} - 2 d x

Frequently Asked Questions (FAQ)

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