What is (\partial)/(\partial x)(((ax+by))/(cx+dy)) ?

The answer to (\partial)/(\partial x)(((ax+by))/(cx+dy)) is (-byc+ayd)/((xc+yd)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(((ax+by))/(cx+dy))

\frac{\partial}{\partial x} (\frac{( a x + b y )}{c x + d y})

\frac{- b yc + a y d}{( x c + y d ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{( a x + b y )}{c x + d y})

Treat

a, b, y, c, d

as constants

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( a x + b y ) ( c x + d y ) - \frac{\partial}{\partial x} ( c x + d y ) ( a x + b y )}{( c x + d y ) ^{2}}

\frac{\partial}{\partial x} (a x + b y) = a

\frac{\partial}{\partial x} (c x + d y) = c

= \frac{a ( c x + d y ) - c ( a x + b y )}{( c x + d y ) ^{2}}

Expand

a (c x + d y) - c (a x + b y) : - b yc + a y d

= \frac{- b yc + a y d}{( x c + y d ) ^{2}}

x y^{^{''}} + y^{^{'}} = 1

\frac{\partial}{\partial x} (6 x sin (x + 2 y - z))

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

\int (csc^{2} (x) + 4) d x

\frac{d}{d x} (x^{2} \cdot e^{2 x})

What is (\partial)/(\partial x)(((ax+by))/(cx+dy)) ?
The answer to (\partial)/(\partial x)(((ax+by))/(cx+dy)) is (-byc+ayd)/((xc+yd)^2)