What is (\partial)/(\partial y)(x^{0.5}y^{0.5}) ?

The answer to (\partial)/(\partial y)(x^{0.5}y^{0.5}) is (0.5x^{1/2})/(y^{0.5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(x^{0.5}y^{0.5})

\frac{\partial}{\partial y} (x^{0.5} y^{0.5})

\frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

Solution steps

\frac{\partial}{\partial y} (x^{0.5} y^{0.5})

Treat

x

as a constant

Take the constant out:

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

= x^{0.5} \frac{\partial}{\partial y} (y^{0.5})

Apply the Power Rule:

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

= x^{0.5} \cdot 0.5 y^{0.5 - 1}

Simplify

x^{\frac{1}{2}} \cdot 0.5 y^{0.5 - 1} : \frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

= \frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

\frac{d}{d x} (cos (3 x^{2} - 2 x))

\int \frac{x ^{3}}{5 x ^{4} - 1} d x

\int \frac{ln ( p )}{p ^{3}} d p

\int (3 x + 4)^{3} d x

n = 0 \sum \infty 16 + 24 + 36 + 54

What is (\partial)/(\partial y)(x^{0.5}y^{0.5}) ?
The answer to (\partial)/(\partial y)(x^{0.5}y^{0.5}) is (0.5x^{1/2})/(y^{0.5)}