What is the derivative of x/((x-3^2)) ?

The derivative of x/((x-3^2)) is (-3-x)/((x-3)^3)

What is the first derivative of x/((x-3^2)) ?

The first derivative of x/((x-3^2)) is (-3-x)/((x-3)^3)

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\frac{d}{d x} (\frac{x}{( x - 3 ) ^{2}})

\frac{- 3 - x}{( x - 3 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x}{( x - 3 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x - 3 ) ^{2} - \frac{d}{d x} ( ( x - 3 ) ^{2} ) x}{( ( x - 3 ) ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 3)^{2}) = 2 (x - 3)

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

Simplify

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

= \frac{- 3 - x}{( x - 3 ) ^{3}}

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