What is the derivative of (x^4+36x^2)/((x^2+12)^2) ?

The derivative of (x^4+36x^2)/((x^2+12)^2) is (24x(-x^2+36))/((x^2+12)^3)

What is the first derivative of (x^4+36x^2)/((x^2+12)^2) ?

The first derivative of (x^4+36x^2)/((x^2+12)^2) is (24x(-x^2+36))/((x^2+12)^3)

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derivative of

\frac{x ^{4} + 36 x ^{2}}{( x ^{2} + 12 ) ^{2}}

\frac{24 x ( - x ^{2} + 36 )}{( x ^{2} + 12 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{4} + 36 x ^{2}}{( x ^{2} + 12 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{4} + 36 x ^{2} ) ( x ^{2} + 12 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 12 ) ^{2} ) ( x ^{4} + 36 x ^{2} )}{( ( x ^{2} + 12 ) ^{2} ) ^{2}}

\frac{d}{d x} (x^{4} + 36 x^{2}) = 4 x^{3} + 72 x

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

= \frac{( 4 x ^{3} + 72 x ) ( x ^{2} + 12 ) ^{2} - 4 x ( x ^{2} + 12 ) ( x ^{4} + 36 x ^{2} )}{( ( x ^{2} + 12 ) ^{2} ) ^{2}}

Simplify

\frac{( 4 x ^{3} + 72 x ) ( x ^{2} + 12 ) ^{2} - 4 x ( x ^{2} + 12 ) ( x ^{4} + 36 x ^{2} )}{( ( x ^{2} + 12 ) ^{2} ) ^{2}} : \frac{24 x ( - x ^{2} + 36 )}{( x ^{2} + 12 ) ^{3}}

= \frac{24 x ( - x ^{2} + 36 )}{( x ^{2} + 12 ) ^{3}}

x \to 2 lim (e^{x^{2} - 2 x})

\int \frac{x}{5 x - 4} d x

\int x (a^{2} - x^{2}) d x

f (x) = \frac{1}{2} x^{2}

\frac{\partial}{\partial y} (ln (x^{8} y))

What is the derivative of (x^4+36x^2)/((x^2+12)^2) ?
The derivative of (x^4+36x^2)/((x^2+12)^2) is (24x(-x^2+36))/((x^2+12)^3)
What is the first derivative of (x^4+36x^2)/((x^2+12)^2) ?
The first derivative of (x^4+36x^2)/((x^2+12)^2) is (24x(-x^2+36))/((x^2+12)^3)