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Popular >

derivative of ln(x^2-9x+1)

Solution

\frac{d}{d x} (ln (x^{2} - 9 x + 1))

Solution

\frac{2 x - 9}{x ^{2} - 9 x + 1}

Solution steps

\frac{d}{d x} (ln (x^{2} - 9 x + 1))

Apply the chain rule:

\frac{1}{x ^{2} - 9 x + 1} \frac{d}{d x} (x^{2} - 9 x + 1)

= \frac{1}{x ^{2} - 9 x + 1} \frac{d}{d x} (x^{2} - 9 x + 1)

\frac{d}{d x} (x^{2} - 9 x + 1) = 2 x - 9

= \frac{1}{x ^{2} - 9 x + 1} (2 x - 9)

Simplify

\frac{1}{x ^{2} - 9 x + 1} (2 x - 9) : \frac{2 x - 9}{x ^{2} - 9 x + 1}

= \frac{2 x - 9}{x ^{2} - 9 x + 1}

Popular Examples

sum from n=0 to infinity}(n^{10 of*10^n)/(n!)

n = 0 \sum \infty \frac{n ^{10} \cdot 1 0 ^{n}}{n !}

integral of 1/(sqrt(x^2-6x+10))

\int \frac{1}{x ^{2} - 6 x + 10} d x

integral of x^2-2x-15

\int x^{2} - 2 x - 15 d x

(\partial)/(\partial y)(y/(y+4x))

\frac{\partial}{\partial y} (\frac{y}{y + 4 x})

derivative of (2e^x/(5x))

\frac{d}{d x} (\frac{2 e ^{x}}{5 x})

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^2-9x+1) ?
The derivative of ln(x^2-9x+1) is (2x-9)/(x^2-9x+1)
What is the first derivative of ln(x^2-9x+1) ?
The first derivative of ln(x^2-9x+1) is (2x-9)/(x^2-9x+1)