What is (\partial)/(\partial x)(2/(1+x^3)) ?

The answer to (\partial)/(\partial x)(2/(1+x^3)) is -(6x^2)/((1+x^3)^2)

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(\partial)/(\partial x)(2/(1+x^3))

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{6 x ^{2}}{( 1 + x ^{3} ) ^{2}}

\int x ln^{2} (d) x d x

\frac{d}{d x} (arccot (x^{2}))

\frac{d}{d x} (3 e^{- 5 x})

f (x) = x^{3} - 12 x^{2} + 45 x

\int \frac{x ^{2}}{2 x - 1} d x

What is (\partial)/(\partial x)(2/(1+x^3)) ?
The answer to (\partial)/(\partial x)(2/(1+x^3)) is -(6x^2)/((1+x^3)^2)