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

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

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

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

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derivative of

\frac{3 x + 1}{x ^{2} + 2 x + 2}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

x \to 0 lim (x - 2)

\int sin (e^{- x}) d x

\frac{\partial}{\partial x} (2 x^{2} + y^{2} - 5 y)

e^{- 2 x} x^{3} (- x + 2)

\int t^{7} e^{- t^{8}} d t

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