What is the derivative of f(x)= 9/(x-6) ?

The derivative of f(x)= 9/(x-6) is -9/((x-6)^2)

What is the first derivative of f(x)= 9/(x-6) ?

The first derivative of f(x)= 9/(x-6) is -9/((x-6)^2)

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derivative

- \frac{9}{( x - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{9}{x - 6})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{x - 6})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 9 \frac{d}{d x} ((x - 6)^{- 1})

Apply the chain rule:

- \frac{1}{( x - 6 ) ^{2}} \frac{d}{d x} (x - 6)

= - \frac{1}{( x - 6 ) ^{2}} \frac{d}{d x} (x - 6)

\frac{d}{d x} (x - 6) = 1

= 9 (- \frac{1}{( x - 6 ) ^{2}} \cdot 1)

Simplify

9 (- \frac{1}{( x - 6 ) ^{2}} \cdot 1) : - \frac{9}{( x - 6 ) ^{2}}

= - \frac{9}{( x - 6 ) ^{2}}

What is the derivative of f(x)= 9/(x-6) ?
The derivative of f(x)= 9/(x-6) is -9/((x-6)^2)
What is the first derivative of f(x)= 9/(x-6) ?
The first derivative of f(x)= 9/(x-6) is -9/((x-6)^2)