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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} - 8 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = 5

\int_{- \infty}^{0} x e^{9 x} d x

\frac{\partial}{\partial y} (y^{3} - y)

f (x) = x^{2} - 8

\frac{s + 1}{s ^{2} ( s + 2 ) ^{3}}

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