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}} \cdot 1)

Simplify

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

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

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

\frac{\partial}{\partial y} (e^{2 x} sin (y))

- 4 + 2 e^{x} - 3 x

\int x x^{2} + 2 d x

f (x) = - x^{3} + 3 x^{2}

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)