What is the derivative of-2/((1+x^3)) ?

The derivative of-2/((1+x^3)) is 6/((1+x)^4)

What is the first derivative of-2/((1+x^3)) ?

The first derivative of-2/((1+x^3)) is 6/((1+x)^4)

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

\frac{6}{( 1 + x ) ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{6}{( 1 + x ) ^{4}}

\frac{x ^{2} + 3 x - 3}{3 x ^{2} - 5 x + 1}

x \to 3 lim (\frac{( 3 - x )}{x - 3})

\frac{\partial}{\partial x} (2 x^{3} + 2 y^{2} - 12 x y + 10)

x \to 8 lim (\frac{x + 8}{x - 8})

\int_{0}^{120} 5.5 (120 - x) d x

What is the derivative of-2/((1+x^3)) ?
The derivative of-2/((1+x^3)) is 6/((1+x)^4)
What is the first derivative of-2/((1+x^3)) ?
The first derivative of-2/((1+x^3)) is 6/((1+x)^4)