What is the derivative of 6/(x^2-9) ?

The derivative of 6/(x^2-9) is -(12x)/((x^2-9)^2)

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

The first derivative of 6/(x^2-9) is -(12x)/((x^2-9)^2)

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

- \frac{12 x}{( x ^{2} - 9 ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

6 (- \frac{1}{( x ^{2} - 9 ) ^{2}} \cdot 2 x) : - \frac{12 x}{( x ^{2} - 9 ) ^{2}}

= - \frac{12 x}{( x ^{2} - 9 ) ^{2}}

What is the derivative of 6/(x^2-9) ?
The derivative of 6/(x^2-9) is -(12x)/((x^2-9)^2)
What is the first derivative of 6/(x^2-9) ?
The first derivative of 6/(x^2-9) is -(12x)/((x^2-9)^2)