What is the derivative of (2+x^{-3}) ?

The derivative of (2+x^{-3}) is -3/((2+x)^4)

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= - \frac{3}{( 2 + x ) ^{4}} \cdot 1

Simplify

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

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