What is the derivative of (x^3+5/(x^2+2x+3)) ?

The derivative of (x^3+5/(x^2+2x+3)) is (x^4+4x^3+9x^2-10x-10)/((x^2+2x+3)^2)

What is the first derivative of (x^3+5/(x^2+2x+3)) ?

The first derivative of (x^3+5/(x^2+2x+3)) is (x^4+4x^3+9x^2-10x-10)/((x^2+2x+3)^2)

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\frac{d}{d x} (\frac{x ^{3} + 5}{x ^{2} + 2 x + 3})

\frac{x ^{4} + 4 x ^{3} + 9 x ^{2} - 10 x - 10}{( x ^{2} + 2 x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} + 5}{x ^{2} + 2 x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{3} + 5 ) ( x ^{2} + 2 x + 3 ) - \frac{d}{d x} ( x ^{2} + 2 x + 3 ) ( x ^{3} + 5 )}{( x ^{2} + 2 x + 3 ) ^{2}}

\frac{d}{d x} (x^{3} + 5) = 3 x^{2}

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

= \frac{3 x ^{2} ( x ^{2} + 2 x + 3 ) - ( 2 x + 2 ) ( x ^{3} + 5 )}{( x ^{2} + 2 x + 3 ) ^{2}}

Expand

3 x^{2} (x^{2} + 2 x + 3) - (2 x + 2) (x^{3} + 5) : x^{4} + 4 x^{3} + 9 x^{2} - 10 x - 10

= \frac{x ^{4} + 4 x ^{3} + 9 x ^{2} - 10 x - 10}{( x ^{2} + 2 x + 3 ) ^{2}}

f (x) = x^{3}

\int lo g_{6} (x) d x

\frac{\partial}{\partial x} (4 x y e^{- x^{2} - y^{2}})

\frac{\partial}{\partial x} (x y + 2 x - ln (x^{2} y))

\int (x^{2} + 3) d x

What is the derivative of (x^3+5/(x^2+2x+3)) ?
The derivative of (x^3+5/(x^2+2x+3)) is (x^4+4x^3+9x^2-10x-10)/((x^2+2x+3)^2)
What is the first derivative of (x^3+5/(x^2+2x+3)) ?
The first derivative of (x^3+5/(x^2+2x+3)) is (x^4+4x^3+9x^2-10x-10)/((x^2+2x+3)^2)