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

The derivative of (2x+5/(x^2-3)) is (-2x^2-10x-6)/((x^2-3)^2)

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

The first derivative of (2x+5/(x^2-3)) is (-2x^2-10x-6)/((x^2-3)^2)

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

\frac{- 2 x ^{2} - 10 x - 6}{( x ^{2} - 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 (x^{2} - 3) - 2 x (2 x + 5) : - 2 x^{2} - 10 x - 6

= \frac{- 2 x ^{2} - 10 x - 6}{( x ^{2} - 3 ) ^{2}}

What is the derivative of (2x+5/(x^2-3)) ?
The derivative of (2x+5/(x^2-3)) is (-2x^2-10x-6)/((x^2-3)^2)
What is the first derivative of (2x+5/(x^2-3)) ?
The first derivative of (2x+5/(x^2-3)) is (-2x^2-10x-6)/((x^2-3)^2)