What is the derivative of (6x^3-2/(x^2-4)) ?

The derivative of (6x^3-2/(x^2-4)) is (6x^4-72x^2+4x)/((x^2-4)^2)

What is the first derivative of (6x^3-2/(x^2-4)) ?

The first derivative of (6x^3-2/(x^2-4)) is (6x^4-72x^2+4x)/((x^2-4)^2)

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\frac{d}{d x} (\frac{6 x ^{3} - 2}{x ^{2} - 4})

\frac{6 x ^{4} - 72 x ^{2} + 4 x}{( x ^{2} - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x ^{3} - 2}{x ^{2} - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x ^{3} - 2 ) ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) ( 6 x ^{3} - 2 )}{( x ^{2} - 4 ) ^{2}}

\frac{d}{d x} (6 x^{3} - 2) = 18 x^{2}

\frac{d}{d x} (x^{2} - 4) = 2 x

= \frac{18 x ^{2} ( x ^{2} - 4 ) - 2 x ( 6 x ^{3} - 2 )}{( x ^{2} - 4 ) ^{2}}

Expand

18 x^{2} (x^{2} - 4) - 2 x (6 x^{3} - 2) : 6 x^{4} - 72 x^{2} + 4 x

= \frac{6 x ^{4} - 72 x ^{2} + 4 x}{( x ^{2} - 4 ) ^{2}}

What is the derivative of (6x^3-2/(x^2-4)) ?
The derivative of (6x^3-2/(x^2-4)) is (6x^4-72x^2+4x)/((x^2-4)^2)
What is the first derivative of (6x^3-2/(x^2-4)) ?
The first derivative of (6x^3-2/(x^2-4)) is (6x^4-72x^2+4x)/((x^2-4)^2)