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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derivative of

\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}}

x \to 0 lim (\frac{x - 1}{x ^{2}})

\frac{3}{x} + \frac{5}{x ^{3}}, at x = - 1

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

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2})

\int \frac{2}{( 1 - x ) ^{2}} 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)