What is (\partial)/(\partial y)((3xy)/(x^4+y^4)) ?

The answer to (\partial)/(\partial y)((3xy)/(x^4+y^4)) is (3x(x^4-3y^4))/((x^4+y^4)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)((3xy)/(x^4+y^4))

\frac{\partial}{\partial y} (\frac{3 x y}{x ^{4} + y ^{4}})

\frac{3 x ( x ^{4} - 3 y ^{4} )}{( x ^{4} + y ^{4} ) ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{3 x y}{x ^{4} + y ^{4}})

Treat

x

as a constant

Take the constant out:

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

= 3 x \frac{\partial}{\partial y} (\frac{y}{x ^{4} + y ^{4}})

Apply the Quotient Rule:

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

= 3 x \frac{\frac{\partial}{\partial y} ( y ) ( x ^{4} + y ^{4} ) - \frac{\partial}{\partial y} ( x ^{4} + y ^{4} ) y}{( x ^{4} + y ^{4} ) ^{2}}

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

\frac{\partial}{\partial y} (x^{4} + y^{4}) = 4 y^{3}

= 3 x \frac{1 \cdot ( x ^{4} + y ^{4} ) - 4 y ^{3} y}{( x ^{4} + y ^{4} ) ^{2}}

Simplify

3 x \frac{1 \cdot ( x ^{4} + y ^{4} ) - 4 y ^{3} y}{( x ^{4} + y ^{4} ) ^{2}} : \frac{3 x ( x ^{4} - 3 y ^{4} )}{( x ^{4} + y ^{4} ) ^{2}}

= \frac{3 x ( x ^{4} - 3 y ^{4} )}{( x ^{4} + y ^{4} ) ^{2}}

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

x, - 2 x + 3, 0, 1.5

\frac{d}{d x} (5 cos^{2} (x) - 10 sin (x))

\int (x + 1)^{100} d x

x \to 0 lim (x^{\frac{3}{2}})

What is (\partial)/(\partial y)((3xy)/(x^4+y^4)) ?
The answer to (\partial)/(\partial y)((3xy)/(x^4+y^4)) is (3x(x^4-3y^4))/((x^4+y^4)^2)