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Popular >

derivative of (x^3+4^{-3})

Solution

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

Solution

- \frac{9 x ^{2}}{( x ^{3} + 4 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{3} + 4) = 3 x^{2}

= - \frac{3}{( x ^{3} + 4 ) ^{4}} \cdot 3 x^{2}

Simplify

- \frac{3}{( x ^{3} + 4 ) ^{4}} \cdot 3 x^{2} : - \frac{9 x ^{2}}{( x ^{3} + 4 ) ^{4}}

= - \frac{9 x ^{2}}{( x ^{3} + 4 ) ^{4}}

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Frequently Asked Questions (FAQ)

What is the derivative of (x^3+4^{-3}) ?
The derivative of (x^3+4^{-3}) is -(9x^2)/((x^3+4)^4)
What is the first derivative of (x^3+4^{-3}) ?
The first derivative of (x^3+4^{-3}) is -(9x^2)/((x^3+4)^4)