What is (\partial}{\partial x}(\frac{3y^2)/x) ?

The answer to (\partial}{\partial x}(\frac{3y^2)/x) is -(3y^2)/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial}{\partial x}(\frac{3y^2)/x)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

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

\int (3 x^{5} - x^{3} + 6) d x

\int_{0}^{8} \frac{x}{4} d x

x \to - 7 lim (\frac{x + 2}{x})

\int 64 - 4 x^{2} d x

\int 3 w 4 - w^{2} d w

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