What is the derivative of ln((x+3^2)) ?

The derivative of ln((x+3^2)) is 2/(x+3)

What is the first derivative of ln((x+3^2)) ?

The first derivative of ln((x+3^2)) is 2/(x+3)

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

\frac{2}{x + 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{x + 3}

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