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Popular >

derivative of 1/(x^3+2)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of x^3-2x^2+x-3

x \to 2 lim (x^{3} - 2 x^{2} + x - 3)

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(2 - 3 x^{2})^{4} (x^{7} + 3)^{3}

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f (x) = \frac{x}{4}

derivative of 2+sqrt(5x)

\frac{d}{d x} (2 + 5 x)

sum from n=2 to infinity of n^2-n

n = 2 \sum \infty n^{2} - n

Frequently Asked Questions (FAQ)

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