What is the derivative of 1/(x^2-x-6) ?

The derivative of 1/(x^2-x-6) is -(2x-1)/((x^2-x-6)^2)

What is the first derivative of 1/(x^2-x-6) ?

The first derivative of 1/(x^2-x-6) is -(2x-1)/((x^2-x-6)^2)

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \frac{d y}{d x} = y + x e^{\frac{y}{x}}

\int_{0}^{\frac{π}{3}} sin^{3} (x) d x

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

\int e^{- x} \cdot x d x

\int 6^{s i n (x)} cos (x) d x

What is the derivative of 1/(x^2-x-6) ?
The derivative of 1/(x^2-x-6) is -(2x-1)/((x^2-x-6)^2)
What is the first derivative of 1/(x^2-x-6) ?
The first derivative of 1/(x^2-x-6) is -(2x-1)/((x^2-x-6)^2)