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

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

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

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

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derivative of

f (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{1}{2 - x}

g (x) = \frac{- 7}{x}

x \to - 2 lim (3 x^{3} - 2 x + 7)

\int \frac{1}{t - 20} d t

\int \frac{1}{1 + e ^{- 5 x}} d x

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