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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)((xy^2)/(x+y))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

sec (4 x)

f (x) = cot (x)

\int 2 x + 8 e^{x} d x

\frac{d y}{d t} = \frac{4}{5} y

\frac{d}{d x} (\frac{0.09 ( 5 ^{x} )}{x ^{3}})

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