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

The derivative of (2x-3/(x^2+1)) is (-2x^2+6x+2)/((x^2+1)^2)

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

The first derivative of (2x-3/(x^2+1)) is (-2x^2+6x+2)/((x^2+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

= \frac{- 2 x ^{2} + 6 x + 2}{( x ^{2} + 1 ) ^{2}}

y^{^{'}} = 2 x y + 3 y - 4 x - 6

\int 2 x^{3} d x

x \to \infty lim (- e^{x})

\int e^{2 x} 1 - 4 e^{2 x} d x

\int 2 sin^{3} (3 x) cos^{3} (3 x) d x

What is the derivative of (2x-3/(x^2+1)) ?
The derivative of (2x-3/(x^2+1)) is (-2x^2+6x+2)/((x^2+1)^2)
What is the first derivative of (2x-3/(x^2+1)) ?
The first derivative of (2x-3/(x^2+1)) is (-2x^2+6x+2)/((x^2+1)^2)