What is the derivative of (1-2x^3)/(x^4+3x^2-6) ?

The derivative of (1-2x^3)/(x^4+3x^2-6) is (2x^6-6x^4-4x^3+36x^2-6x)/((x^4+3x^2-6)^2)

What is the first derivative of (1-2x^3)/(x^4+3x^2-6) ?

The first derivative of (1-2x^3)/(x^4+3x^2-6) is (2x^6-6x^4-4x^3+36x^2-6x)/((x^4+3x^2-6)^2)

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derivative of

\frac{1 - 2 x ^{3}}{x ^{4} + 3 x ^{2} - 6}

\frac{2 x ^{6} - 6 x ^{4} - 4 x ^{3} + 36 x ^{2} - 6 x}{( x ^{4} + 3 x ^{2} - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 2 x ^{3}}{x ^{4} + 3 x ^{2} - 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 2 x ^{3} ) ( x ^{4} + 3 x ^{2} - 6 ) - \frac{d}{d x} ( x ^{4} + 3 x ^{2} - 6 ) ( 1 - 2 x ^{3} )}{( x ^{4} + 3 x ^{2} - 6 ) ^{2}}

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

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

= \frac{( - 6 x ^{2} ) ( x ^{4} + 3 x ^{2} - 6 ) - ( 4 x ^{3} + 6 x ) ( 1 - 2 x ^{3} )}{( x ^{4} + 3 x ^{2} - 6 ) ^{2}}

Simplify

\frac{( - 6 x ^{2} ) ( x ^{4} + 3 x ^{2} - 6 ) - ( 4 x ^{3} + 6 x ) ( 1 - 2 x ^{3} )}{( x ^{4} + 3 x ^{2} - 6 ) ^{2}} : \frac{2 x ^{6} - 6 x ^{4} - 4 x ^{3} + 36 x ^{2} - 6 x}{( x ^{4} + 3 x ^{2} - 6 ) ^{2}}

= \frac{2 x ^{6} - 6 x ^{4} - 4 x ^{3} + 36 x ^{2} - 6 x}{( x ^{4} + 3 x ^{2} - 6 ) ^{2}}

\int (- 8 y^{3}) d y

\int t^{3} e^{- 5 t} d t

x \to 1 lim (e^{4 x^{3} - 4 x})

\frac{d}{d x} (((x + x^{9})^{- 6} + 3 x)^{3})

What is the derivative of (1-2x^3)/(x^4+3x^2-6) ?
The derivative of (1-2x^3)/(x^4+3x^2-6) is (2x^6-6x^4-4x^3+36x^2-6x)/((x^4+3x^2-6)^2)
What is the first derivative of (1-2x^3)/(x^4+3x^2-6) ?
The first derivative of (1-2x^3)/(x^4+3x^2-6) is (2x^6-6x^4-4x^3+36x^2-6x)/((x^4+3x^2-6)^2)