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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 3) = 1

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

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

Simplify

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

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

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