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Popular >

derivative of ln(3/(x^2+9))

Solution

\frac{d}{d x} (ln (\frac{3}{x ^{2} + 9}))

Solution

- \frac{2 x}{x ^{2} + 9}

Solution steps

\frac{d}{d x} (ln (\frac{3}{x ^{2} + 9}))

Apply the chain rule:

\frac{1}{\frac{3}{x ^{2} + 9}} \frac{d}{d x} (\frac{3}{x ^{2} + 9})

= \frac{1}{\frac{3}{x ^{2} + 9}} \frac{d}{d x} (\frac{3}{x ^{2} + 9})

\frac{d}{d x} (\frac{3}{x ^{2} + 9}) = - \frac{6 x}{( x ^{2} + 9 ) ^{2}}

= \frac{1}{\frac{3}{x ^{2} + 9}} (- \frac{6 x}{( x ^{2} + 9 ) ^{2}})

Simplify

\frac{1}{\frac{3}{x ^{2} + 9}} (- \frac{6 x}{( x ^{2} + 9 ) ^{2}}) : - \frac{2 x}{x ^{2} + 9}

= - \frac{2 x}{x ^{2} + 9}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(3/(x^2+9)) ?
The derivative of ln(3/(x^2+9)) is -(2x)/(x^2+9)
What is the first derivative of ln(3/(x^2+9)) ?
The first derivative of ln(3/(x^2+9)) is -(2x)/(x^2+9)