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Popular Calculus >

derivative of ln(x^2-7x+1)

Solution

\frac{d}{d x} (ln (x^{2} - 7 x + 1))

Solution

\frac{2 x - 7}{x ^{2} - 7 x + 1}

Solution steps

\frac{d}{d x} (ln (x^{2} - 7 x + 1))

Apply the chain rule:

\frac{1}{x ^{2} - 7 x + 1} \frac{d}{d x} (x^{2} - 7 x + 1)

= \frac{1}{x ^{2} - 7 x + 1} \frac{d}{d x} (x^{2} - 7 x + 1)

\frac{d}{d x} (x^{2} - 7 x + 1) = 2 x - 7

= \frac{1}{x ^{2} - 7 x + 1} (2 x - 7)

Simplify

\frac{1}{x ^{2} - 7 x + 1} (2 x - 7) : \frac{2 x - 7}{x ^{2} - 7 x + 1}

= \frac{2 x - 7}{x ^{2} - 7 x + 1}

Graph

Popular Examples

derivative of (sqrt(6x-x^2)/(tan(x)))

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

integral of e^{9x}

\int e^{9 x} d x

integral of x^4*e^{x^5}

\int x^{4} \cdot e^{x^{5}} d x

integral from 0 to 3 of (4-x^2)

\int_{0}^{3} (4 - x^{2}) d x

(dx)/(dt)=4x(7-x)

\frac{d x}{d t} = 4 x (7 - x)

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^2-7x+1) ?
The derivative of ln(x^2-7x+1) is (2x-7)/(x^2-7x+1)
What is the first derivative of ln(x^2-7x+1) ?
The first derivative of ln(x^2-7x+1) is (2x-7)/(x^2-7x+1)