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

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

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

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

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

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

Solution steps

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

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

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

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

Expand

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

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

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

n = 0 \sum \infty n^{3} x^{n}

\frac{d}{d x} (9 x arcsin (x))

\frac{d}{d x} (6 x - 5)

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

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