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

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

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

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

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

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

Solution steps

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

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

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

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

Expand

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

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

x \to 2 lim (\frac{0}{x - 2})

n = 1 \sum \infty n^{3} \cdot 2^{- n}

\frac{d y}{d t} = y + \frac{3}{y ^{2}}

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

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