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Popular >

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

Solution

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

Solution

\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}

Popular Examples

integral of (x^3+x)/x

\int \frac{x ^{3} + x}{x} d x

(\partial)/(\partial x)(2x+ye^x)

\frac{\partial}{\partial x} (2 x + y e^{x})

integral from 0 to 0.1 of xarctan(3x)

\int_{0}^{0.1} x arctan (3 x) d x

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\frac{d}{d x} (1. 5^{1.7 x})

slope ofintercept (-5,1),(-4,-9)slope intercept

(- 5, 1), (- 4, - 9)

Frequently Asked Questions (FAQ)

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)