What is the derivative of f(x)= 1/(x^3+2x+1) ?

The derivative of f(x)= 1/(x^3+2x+1) is -(3x^2+2)/((x^3+2x+1)^2)

What is the first derivative of f(x)= 1/(x^3+2x+1) ?

The first derivative of f(x)= 1/(x^3+2x+1) is -(3x^2+2)/((x^3+2x+1)^2)

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derivative of

f (x) = \frac{1}{x ^{3} + 2 x + 1}

- \frac{3 x ^{2} + 2}{( x ^{3} + 2 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{3} + 2 x + 1})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{3} + 2 x + 1)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{3} + 2 x + 1 ) ^{2}} \frac{d}{d x} (x^{3} + 2 x + 1)

= - \frac{1}{( x ^{3} + 2 x + 1 ) ^{2}} \frac{d}{d x} (x^{3} + 2 x + 1)

\frac{d}{d x} (x^{3} + 2 x + 1) = 3 x^{2} + 2

= - \frac{1}{( x ^{3} + 2 x + 1 ) ^{2}} (3 x^{2} + 2)

Simplify

- \frac{1}{( x ^{3} + 2 x + 1 ) ^{2}} (3 x^{2} + 2) : - \frac{3 x ^{2} + 2}{( x ^{3} + 2 x + 1 ) ^{2}}

= - \frac{3 x ^{2} + 2}{( x ^{3} + 2 x + 1 ) ^{2}}

ln (x^{3} + 3 x^{2} + 5 x + 6)

\frac{d}{d x} (2 x y - 1)

x \to 3 lim (2 x - 8)

\frac{d}{d x} (\frac{600 x}{2 x ^{2} + 25})

\int \frac{8 x ^{2}}{4 x + 6} d x

What is the derivative of f(x)= 1/(x^3+2x+1) ?
The derivative of f(x)= 1/(x^3+2x+1) is -(3x^2+2)/((x^3+2x+1)^2)
What is the first derivative of f(x)= 1/(x^3+2x+1) ?
The first derivative of f(x)= 1/(x^3+2x+1) is -(3x^2+2)/((x^3+2x+1)^2)