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Popular >

derivative of 1/((3+x^3))

Solution

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

Solution

- \frac{3}{( 3 + x ) ^{4}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{( 3 + x ) ^{4}} \frac{d}{d x} (3 + x)

= - \frac{3}{( 3 + x ) ^{4}} \frac{d}{d x} (3 + x)

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

= - \frac{3}{( 3 + x ) ^{4}} \cdot 1

Simplify

= - \frac{3}{( 3 + x ) ^{4}}

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x \to 6 lim (\frac{x ^{2} - 3}{x - 6})

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x \to \infty lim (6 (1 + \frac{1}{x})^{x^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of 1/((3+x^3)) ?
The derivative of 1/((3+x^3)) is -3/((3+x)^4)
What is the first derivative of 1/((3+x^3)) ?
The first derivative of 1/((3+x^3)) is -3/((3+x)^4)