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

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

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^3y^6))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{y ^{6}} \frac{\partial}{\partial x} (\frac{x}{x ^{3}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x cos (x) + π)

y^{^{''}} - 2 y^{^{'}} - 3 y = - 5 t e - t

3 x + 5

y^{^{'}} + 6 (tan (6 x)) y = 4 cos (6 x)

\int sin (x) e^{- 2 x} d x

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