What is the derivative of ln((x+3^4)) ?

The derivative of ln((x+3^4)) is 4/(x+3)

What is the first derivative of ln((x+3^4)) ?

The first derivative of ln((x+3^4)) is 4/(x+3)

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\frac{d}{d x} (ln ((x + 3)^{4}))

\frac{4}{x + 3}

Solution steps

\frac{d}{d x} (ln ((x + 3)^{4}))

Apply the chain rule:

\frac{1}{( x + 3 ) ^{4}} \frac{d}{d x} ((x + 3)^{4})

= \frac{1}{( x + 3 ) ^{4}} \frac{d}{d x} ((x + 3)^{4})

\frac{d}{d x} ((x + 3)^{4}) = 4 (x + 3)^{3}

= \frac{1}{( x + 3 ) ^{4}} \cdot 4 (x + 3)^{3}

Simplify

\frac{1}{( x + 3 ) ^{4}} \cdot 4 (x + 3)^{3} : \frac{4}{x + 3}

= \frac{4}{x + 3}

What is the derivative of ln((x+3^4)) ?
The derivative of ln((x+3^4)) is 4/(x+3)
What is the first derivative of ln((x+3^4)) ?
The first derivative of ln((x+3^4)) is 4/(x+3)