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Popular >

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

Solution

derivative of

ln (x^{2} - x + 1)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (2x^2)/(x^4-1)

\int \frac{2 x ^{2}}{x ^{4} - 1} d x

y^{''}+1/2 y^'+1/16 y=0,y(0)=5,y^'(0)=0

y^{^{''}} + \frac{1}{2} y^{^{'}} + \frac{1}{16} y = 0, y (0) = 5, y^{^{'}} (0) = 0

limit as x approaches 0 of (x^3)/(x^6)

x \to 0 lim (\frac{x ^{3}}{x ^{6}})

(\partial)/(\partial y)(x^2+2y^2-x)

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

integral of (2x-3)/(sqrt(4x-x^2))

\int \frac{2 x - 3}{4 x - x ^{2}} d x

Frequently Asked Questions (FAQ)

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