What is (\partial)/(\partial x)((x+6y)/(y^2+3x^2)) ?

The answer to (\partial)/(\partial x)((x+6y)/(y^2+3x^2)) is (y^2-3x^2-36xy)/((y^2+3x^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((x+6y)/(y^2+3x^2))

\frac{\partial}{\partial x} (\frac{x + 6 y}{y ^{2} + 3 x ^{2}})

\frac{y ^{2} - 3 x ^{2} - 36 x y}{( y ^{2} + 3 x ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 6 y}{y ^{2} + 3 x ^{2}})

Treat

y

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( x + 6 y ) ( y ^{2} + 3 x ^{2} ) - \frac{\partial}{\partial x} ( y ^{2} + 3 x ^{2} ) ( x + 6 y )}{( y ^{2} + 3 x ^{2} ) ^{2}}

\frac{\partial}{\partial x} (x + 6 y) = 1

\frac{\partial}{\partial x} (y^{2} + 3 x^{2}) = 6 x

= \frac{1 \cdot ( y ^{2} + 3 x ^{2} ) - 6 x ( x + 6 y )}{( y ^{2} + 3 x ^{2} ) ^{2}}

Simplify

\frac{1 \cdot ( y ^{2} + 3 x ^{2} ) - 6 x ( x + 6 y )}{( y ^{2} + 3 x ^{2} ) ^{2}} : \frac{y ^{2} - 3 x ^{2} - 36 x y}{( y ^{2} + 3 x ^{2} ) ^{2}}

= \frac{y ^{2} - 3 x ^{2} - 36 x y}{( y ^{2} + 3 x ^{2} ) ^{2}}

\int_{1}^{4} \frac{2}{x ^{2} + 4 x + 4} d x

3 t - e^{- 3 t}

\frac{\partial}{\partial x} (cos (8 y - 2 x))

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

\int 9 x e^{- x} d x

What is (\partial)/(\partial x)((x+6y)/(y^2+3x^2)) ?
The answer to (\partial)/(\partial x)((x+6y)/(y^2+3x^2)) is (y^2-3x^2-36xy)/((y^2+3x^2)^2)