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

The answer to (\partial)/(\partial x)(2/(1-3x^3)) is (18x^2)/((1-3x^3)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{18 x ^{2}}{( 1 - 3 x ^{3} ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (1 - 3 x^{3}) = - 9 x^{2}

= 2 (- \frac{1}{( 1 - 3 x ^{3} ) ^{2}} (- 9 x^{2}))

Simplify

2 (- \frac{1}{( 1 - 3 x ^{3} ) ^{2}} (- 9 x^{2})) : \frac{18 x ^{2}}{( 1 - 3 x ^{3} ) ^{2}}

= \frac{18 x ^{2}}{( 1 - 3 x ^{3} ) ^{2}}

\frac{d y}{d x} = x y + 12 x

y = \frac{1}{1 + x ^{2}}

\frac{d x}{d y} = - \frac{8 y ^{2} + 10 x y}{5 y ^{2} + 2 x}

\frac{\partial}{\partial x} (\frac{x ^{2}}{2} + y^{4})

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

What is (\partial)/(\partial x)(2/(1-3x^3)) ?
The answer to (\partial)/(\partial x)(2/(1-3x^3)) is (18x^2)/((1-3x^3)^2)