What is (\partial)/(\partial x)(x/(x^3-y^6)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x/(x^3-y^6))

\frac{\partial}{\partial x} (\frac{x}{x ^{3} - y ^{6}})

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

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{3} - y ^{6}})

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( x ) ( x ^{3} - y ^{6} ) - \frac{\partial}{\partial x} ( x ^{3} - y ^{6} ) x}{( x ^{3} - y ^{6} ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x^{3} - y^{6}) = 3 x^{2}

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

1 \cdot (x^{3} - y^{6}) - 3 x^{2} x = - 2 x^{3} - y^{6}

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

\frac{\partial}{\partial x} (7 sec (x) - 4 x)

y^{^{'}} = \frac{4 x ^{2} + 3 y ^{2}}{2 x y}

x^{2} - 8, - x^{2} + 2 x + 4

\frac{d}{d x} (ln (\frac{2 - x}{1 - x}))

\frac{d y}{d x} = \frac{( 1 + x )}{x y ^{16}}

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