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Popular >

derivative of ln|x^2+9|

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{∣ x ^{2} + 9 ∣} \cdot \frac{2 x ( x ^{2} + 9 )}{∣ x ^{2} + 9 ∣}

Simplify

\frac{1}{∣ x ^{2} + 9 ∣} \cdot \frac{2 x ( x ^{2} + 9 )}{∣ x ^{2} + 9 ∣} : \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|x^2+9| ?
The derivative of ln|x^2+9| is (2x)/(x^2+9)
What is the first derivative of ln|x^2+9| ?
The first derivative of ln|x^2+9| is (2x)/(x^2+9)