What is the derivative of 2/((2-x^3)) ?

The derivative of 2/((2-x^3)) is 6/((2-x)^4)

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

The first derivative of 2/((2-x^3)) is 6/((2-x)^4)

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

\frac{6}{( 2 - x ) ^{4}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

= 2 \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

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

Simplify

2 (- \frac{3}{( 2 - x ) ^{4}} (- 1)) : \frac{6}{( 2 - x ) ^{4}}

= \frac{6}{( 2 - x ) ^{4}}

What is the derivative of 2/((2-x^3)) ?
The derivative of 2/((2-x^3)) is 6/((2-x)^4)
What is the first derivative of 2/((2-x^3)) ?
The first derivative of 2/((2-x^3)) is 6/((2-x)^4)