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

The derivative of (x^2-2/(x^3+3x^2)) is -(x^3-6x-12)/(x^3(x+3)^2)

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

The first derivative of (x^2-2/(x^3+3x^2)) is -(x^3-6x-12)/(x^3(x+3)^2)

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

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

Solution steps

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

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

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

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

Simplify

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

= - \frac{x ^{3} - 6 x - 12}{x ^{3} ( x + 3 ) ^{2}}

y = \frac{x + x ^{3}}{x ^{2}}

f (x) = 7 - 2 x

\frac{\partial}{\partial x} (2 x^{3} + 4 y - 2 z^{2})

\int 2 \cdot x \cdot ln (4 x) d x

\int y x d x

What is the derivative of (x^2-2/(x^3+3x^2)) ?
The derivative of (x^2-2/(x^3+3x^2)) is -(x^3-6x-12)/(x^3(x+3)^2)
What is the first derivative of (x^2-2/(x^3+3x^2)) ?
The first derivative of (x^2-2/(x^3+3x^2)) is -(x^3-6x-12)/(x^3(x+3)^2)