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

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

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

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

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

\frac{3}{x + 2}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3}{x + 2}

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