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

The derivative of 2/(sqrt(x^3+1)) is -(3x^2)/((x^3+1)^{3/2)}

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

The first derivative of 2/(sqrt(x^3+1)) is -(3x^2)/((x^3+1)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y - x y^{^{'}} = a (1 + x^{2} y^{^{'}})

x \to 3 lim (\frac{2 x - 9}{x - 3})

\frac{\partial}{\partial x} (x^{3} y z^{2} + 8 yz)

\int \frac{1}{cos ^{2} ( x ) + 5 cos ( x ) + 6} d x

\int 10 x^{3} + 2 x^{2} + \frac{1}{2} x + 3 d x

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