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

The derivative of (6x^3/(3x^2-3)) is (2x^2(x+sqrt(3))(x-sqrt(3)))/((x+1)^2(x-1)^2)

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

The first derivative of (6x^3/(3x^2-3)) is (2x^2(x+sqrt(3))(x-sqrt(3)))/((x+1)^2(x-1)^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

6 \cdot \frac{3 x ^{2} ( 3 x ^{2} - 3 ) - 6 x x ^{3}}{( 3 x ^{2} - 3 ) ^{2}} : \frac{2 x ^{2} ( x + 3 ) ( x - 3 )}{( x + 1 ) ^{2} ( x - 1 ) ^{2}}

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

\frac{\partial}{\partial x} (- 2 x y (6 - x - y))

x \to 2 lim (\frac{- 4}{2 - x})

x \to 0 lim (lo g_{3} (x))

4 x + 1

\frac{d}{d m} (16 m^{2} + 40 m + 25)

What is the derivative of (6x^3/(3x^2-3)) ?
The derivative of (6x^3/(3x^2-3)) is (2x^2(x+sqrt(3))(x-sqrt(3)))/((x+1)^2(x-1)^2)
What is the first derivative of (6x^3/(3x^2-3)) ?
The first derivative of (6x^3/(3x^2-3)) is (2x^2(x+sqrt(3))(x-sqrt(3)))/((x+1)^2(x-1)^2)