What is the derivative of f(x)= x/(x-9) ?

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

What is the first derivative of f(x)= x/(x-9) ?

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

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derivative of

f (x) = \frac{x}{x - 9}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 9) = 1

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

Simplify

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

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

\frac{4 2}{3} t^{\frac{3}{2}}

\int_{0}^{3} \frac{1}{64 + x ^{2}} d x

arcsin (\frac{x}{3})

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

n = 0 \sum \infty - 1

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