What is the derivative of ln((x+6^{11})) ?

The derivative of ln((x+6^{11})) is (11)/(x+6)

What is the first derivative of ln((x+6^{11})) ?

The first derivative of ln((x+6^{11})) is (11)/(x+6)

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\frac{d}{d x} (ln ((x + 6)^{11}))

\frac{11}{x + 6}

Solution steps

\frac{d}{d x} (ln ((x + 6)^{11}))

Apply the chain rule:

\frac{1}{( x + 6 ) ^{11}} \frac{d}{d x} ((x + 6)^{11})

= \frac{1}{( x + 6 ) ^{11}} \frac{d}{d x} ((x + 6)^{11})

\frac{d}{d x} ((x + 6)^{11}) = 11 (x + 6)^{10}

= \frac{1}{( x + 6 ) ^{11}} \cdot 11 (x + 6)^{10}

Simplify

\frac{1}{( x + 6 ) ^{11}} \cdot 11 (x + 6)^{10} : \frac{11}{x + 6}

= \frac{11}{x + 6}

What is the derivative of ln((x+6^{11})) ?
The derivative of ln((x+6^{11})) is (11)/(x+6)
What is the first derivative of ln((x+6^{11})) ?
The first derivative of ln((x+6^{11})) is (11)/(x+6)