What is the derivative of x/((x-9^2)) ?

The derivative of x/((x-9^2)) is (-9-x)/((x-9)^3)

What is the first derivative of x/((x-9^2)) ?

The first derivative of x/((x-9^2)) is (-9-x)/((x-9)^3)

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\frac{d}{d x} (\frac{x}{( x - 9 ) ^{2}})

\frac{- 9 - x}{( x - 9 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x}{( x - 9 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x - 9 ) ^{2} - \frac{d}{d x} ( ( x - 9 ) ^{2} ) x}{( ( x - 9 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x - 9)^{2}) = 2 (x - 9)

= \frac{1 \cdot ( x - 9 ) ^{2} - 2 ( x - 9 ) x}{( ( x - 9 ) ^{2} ) ^{2}}

Simplify

\frac{1 \cdot ( x - 9 ) ^{2} - 2 ( x - 9 ) x}{( ( x - 9 ) ^{2} ) ^{2}} : \frac{- 9 - x}{( x - 9 ) ^{3}}

= \frac{- 9 - x}{( x - 9 ) ^{3}}

\frac{d}{d x} (\frac{8 x ^{2} + 9}{x ^{2} + 1})

\frac{\partial}{\partial y} (\frac{1}{2} y)

\int - 3 tan^{3} (x) d x

6 y^{^{''}} + 11 y^{^{'}} - 2 y = 0

\int x^{2} 6^{2} - x^{2} d x

What is the derivative of x/((x-9^2)) ?
The derivative of x/((x-9^2)) is (-9-x)/((x-9)^3)
What is the first derivative of x/((x-9^2)) ?
The first derivative of x/((x-9^2)) is (-9-x)/((x-9)^3)