What is the derivative of (12)/(x^2(x-3)) ?

The derivative of (12)/(x^2(x-3)) is -(36(x-2))/(x^3(x-3)^2)

What is the first derivative of (12)/(x^2(x-3)) ?

The first derivative of (12)/(x^2(x-3)) is -(36(x-2))/(x^3(x-3)^2)

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derivative of

\frac{12}{x ^{2} ( x - 3 )}

- \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{12}{x ^{2} ( x - 3 )})

Take the constant out:

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

= 12 \frac{d}{d x} (\frac{1}{x ^{2} ( x - 3 )})

Apply exponent rule:

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

= 12 \frac{d}{d x} ((x^{2} (x - 3))^{- 1})

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} (x - 3)) = 3 x^{2} - 6 x

= 12 (- \frac{1}{( x ^{2} ( x - 3 ) ) ^{2}} (3 x^{2} - 6 x))

Simplify

12 (- \frac{1}{( x ^{2} ( x - 3 ) ) ^{2}} (3 x^{2} - 6 x)) : - \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

= - \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

What is the derivative of (12)/(x^2(x-3)) ?
The derivative of (12)/(x^2(x-3)) is -(36(x-2))/(x^3(x-3)^2)
What is the first derivative of (12)/(x^2(x-3)) ?
The first derivative of (12)/(x^2(x-3)) is -(36(x-2))/(x^3(x-3)^2)