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Popular >

derivative of ln(-x^2+6x)

Solution

\frac{d}{d x} (ln (- x^{2} + 6 x))

Solution

\frac{- 2 x + 6}{- x ^{2} + 6 x}

Solution steps

\frac{d}{d x} (ln (- x^{2} + 6 x))

Apply the chain rule:

\frac{1}{- x ^{2} + 6 x} \frac{d}{d x} (- x^{2} + 6 x)

= \frac{1}{- x ^{2} + 6 x} \frac{d}{d x} (- x^{2} + 6 x)

\frac{d}{d x} (- x^{2} + 6 x) = - 2 x + 6

= \frac{1}{- x ^{2} + 6 x} (- 2 x + 6)

Simplify

\frac{1}{- x ^{2} + 6 x} (- 2 x + 6) : \frac{- 2 x + 6}{- x ^{2} + 6 x}

= \frac{- 2 x + 6}{- x ^{2} + 6 x}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(-x^2+6x) ?
The derivative of ln(-x^2+6x) is (-2x+6)/(-x^2+6x)
What is the first derivative of ln(-x^2+6x) ?
The first derivative of ln(-x^2+6x) is (-2x+6)/(-x^2+6x)