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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x + 2) = 1

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

Simplify

\frac{( 3 x ^{2} - 6 x ) ( x + 2 ) - 1 \cdot ( x ^{3} - 3 x ^{2} - 3 )}{( x + 2 ) ^{2}} : \frac{2 x ^{3} + 3 x ^{2} - 12 x + 3}{( x + 2 ) ^{2}}

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

\int \frac{x ^{8}}{x ^{3} + 2} d x

4 x^{4} + 3 x^{3} + 2 x^{2} + x + 1, 1

\frac{\partial}{\partial x} (- 5 y e^{x})

\frac{( s + 2 )}{s ( s ^{2} + 9 )}

\frac{d}{d x} (1 2^{x})

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