What is the derivative of (f(x)g(x))/(f(x)-g(x)) ?

The derivative of (f(x)g(x))/(f(x)-g(x)) is -(x^3g^2)/((fx-xg)^2)

What is the first derivative of (f(x)g(x))/(f(x)-g(x)) ?

The first derivative of (f(x)g(x))/(f(x)-g(x)) is -(x^3g^2)/((fx-xg)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{f ( x ) g ( x )}{f ( x ) - g ( x )}

- \frac{x ^{3} g ^{2}}{( f x - xg ) ^{2}}

Solution steps

\frac{d}{df} (\frac{f xgx}{f x - gx})

Treat

x, g

as constants

Take the constant out:

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

= xgx \frac{d}{df} (\frac{f}{f x - gx})

Apply the Quotient Rule:

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

= xgx \frac{\frac{df}{df} ( f x - gx ) - \frac{d}{df} ( f x - gx ) f}{( f x - gx ) ^{2}}

\frac{df}{df} = 1

\frac{d}{df} (f x - gx) = x

= xgx \frac{1 \cdot ( f x - gx ) - x f}{( f x - gx ) ^{2}}

Simplify

xgx \frac{1 \cdot ( f x - gx ) - x f}{( f x - gx ) ^{2}} : - \frac{x ^{3} g ^{2}}{( f x - xg ) ^{2}}

= - \frac{x ^{3} g ^{2}}{( f x - xg ) ^{2}}

y^{^{'}} = 5 y + a

\frac{d}{d x} (cos (4 x^{3}))

y^{^{'}} + \frac{y}{2 + 3 t} = 3

\int \frac{e ^{2 x}}{e ^{x} + e ^{- x}} d x

\int (x^{2} - 1) sin (2 x) d x

What is the derivative of (f(x)g(x))/(f(x)-g(x)) ?
The derivative of (f(x)g(x))/(f(x)-g(x)) is -(x^3g^2)/((fx-xg)^2)
What is the first derivative of (f(x)g(x))/(f(x)-g(x)) ?
The first derivative of (f(x)g(x))/(f(x)-g(x)) is -(x^3g^2)/((fx-xg)^2)