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

The derivative of (x^2+x+1/(x^2+3)) is (-x^2+4x+3)/((x^2+3)^2)

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

The first derivative of (x^2+x+1/(x^2+3)) is (-x^2+4x+3)/((x^2+3)^2)

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

\frac{- x ^{2} + 4 x + 3}{( x ^{2} + 3 ) ^{2}}

Solution steps

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

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

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

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

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

Expand

(2 x + 1) (x^{2} + 3) - 2 x (x^{2} + x + 1) : - x^{2} + 4 x + 3

= \frac{- x ^{2} + 4 x + 3}{( x ^{2} + 3 ) ^{2}}

(15, 250), (25, 28)

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

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

(0) (4.2)

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

What is the derivative of (x^2+x+1/(x^2+3)) ?
The derivative of (x^2+x+1/(x^2+3)) is (-x^2+4x+3)/((x^2+3)^2)
What is the first derivative of (x^2+x+1/(x^2+3)) ?
The first derivative of (x^2+x+1/(x^2+3)) is (-x^2+4x+3)/((x^2+3)^2)