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

The derivative of (3x-1/(x^2+3)) is (-3x^2+2x+9)/((x^2+3)^2)

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

The first derivative of (3x-1/(x^2+3)) is (-3x^2+2x+9)/((x^2+3)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

3 (x^{2} + 3) - 2 x (3 x - 1) : - 3 x^{2} + 2 x + 9

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

What is the derivative of (3x-1/(x^2+3)) ?
The derivative of (3x-1/(x^2+3)) is (-3x^2+2x+9)/((x^2+3)^2)
What is the first derivative of (3x-1/(x^2+3)) ?
The first derivative of (3x-1/(x^2+3)) is (-3x^2+2x+9)/((x^2+3)^2)