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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

Simplify

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

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

f (x) = cos (tan^{3} (x))

\int 21 sec^{- 2} (x t a) n^{3} x d x

\frac{d}{d θ} (e^{t a n (θ)})

\int \frac{6}{2 x + 3 x ^{2}} d x

\int \frac{x ^{2} + 5}{x ^{3} - x ^{2} + x + 3} d x

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