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)

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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}}

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)