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}

x

\frac{d}{d x} (\frac{1}{x ^{7}} + \frac{1}{x ^{8}})

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

n = 1 \sum \infty n e^{7 n}

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

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)