What is the derivative of (x^4-12x^2/((x^2-4)^2)) ?

The derivative of (x^4-12x^2/((x^2-4)^2)) is (8x(x^2+12))/((x^2-4)^3)

What is the first derivative of (x^4-12x^2/((x^2-4)^2)) ?

The first derivative of (x^4-12x^2/((x^2-4)^2)) is (8x(x^2+12))/((x^2-4)^3)

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\frac{d}{d x} (\frac{x ^{4} - 12 x ^{2}}{( x ^{2} - 4 ) ^{2}})

\frac{8 x ( x ^{2} + 12 )}{( x ^{2} - 4 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{4} - 12 x ^{2}}{( x ^{2} - 4 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{4} - 12 x ^{2} ) ( x ^{2} - 4 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 4 ) ^{2} ) ( x ^{4} - 12 x ^{2} )}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

\frac{d}{d x} (x^{4} - 12 x^{2}) = 4 x^{3} - 24 x

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

= \frac{( 4 x ^{3} - 24 x ) ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) ( x ^{4} - 12 x ^{2} )}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

Simplify

\frac{( 4 x ^{3} - 24 x ) ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) ( x ^{4} - 12 x ^{2} )}{( ( x ^{2} - 4 ) ^{2} ) ^{2}} : \frac{8 x ( x ^{2} + 12 )}{( x ^{2} - 4 ) ^{3}}

= \frac{8 x ( x ^{2} + 12 )}{( x ^{2} - 4 ) ^{3}}

\frac{\partial}{\partial x} (arcsin (\frac{a}{b} sin (x)))

\frac{48}{s ^{5}}

\int e^{2 x^{3} - 1} x^{2} d x

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

x \to 0 lim (\frac{x ^{2} - 1}{x + 1})

What is the derivative of (x^4-12x^2/((x^2-4)^2)) ?
The derivative of (x^4-12x^2/((x^2-4)^2)) is (8x(x^2+12))/((x^2-4)^3)
What is the first derivative of (x^4-12x^2/((x^2-4)^2)) ?
The first derivative of (x^4-12x^2/((x^2-4)^2)) is (8x(x^2+12))/((x^2-4)^3)