What is (\partial)/(\partial y)(x^2sqrt(y)) ?

The answer to (\partial)/(\partial y)(x^2sqrt(y)) is (x^2)/(2sqrt(y))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(x^2sqrt(y))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply the Power Rule:

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

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

Simplify

x^{2} \frac{1}{2} y^{\frac{1}{2} - 1} : \frac{x ^{2}}{2 y}

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

\int \frac{x}{2 - x ^{2}} d x

\frac{d}{d x} (- 3 sin (x - π) + x)

y^{^{'}} - 9 y = 27

\frac{d}{d x} (\frac{1}{5} x)

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

What is (\partial)/(\partial y)(x^2sqrt(y)) ?
The answer to (\partial)/(\partial y)(x^2sqrt(y)) is (x^2)/(2sqrt(y))