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Popular >

derivative of ln(((2)/(3-x^2)))

Solution

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

Solution

\frac{2 x}{3 - x ^{2}}

Solution steps

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

Apply the chain rule:

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

= \frac{1}{\frac{2}{3 - x ^{2}}} \frac{d}{d x} (\frac{2}{3 - x ^{2}})

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

= \frac{1}{\frac{2}{3 - x ^{2}}} \cdot \frac{4 x}{( 3 - x ^{2} ) ^{2}}

Simplify

\frac{1}{\frac{2}{3 - x ^{2}}} \cdot \frac{4 x}{( 3 - x ^{2} ) ^{2}} : \frac{2 x}{3 - x ^{2}}

= \frac{2 x}{3 - x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(((2)/(3-x^2))) ?
The derivative of ln(((2)/(3-x^2))) is (2x)/(3-x^2)
What is the first derivative of ln(((2)/(3-x^2))) ?
The first derivative of ln(((2)/(3-x^2))) is (2x)/(3-x^2)