What is the derivative of (x+1)/(3x^2+6x+7) ?

The derivative of (x+1)/(3x^2+6x+7) is (-3x^2-6x+1)/((3x^2+6x+7)^2)

What is the first derivative of (x+1)/(3x^2+6x+7) ?

The first derivative of (x+1)/(3x^2+6x+7) is (-3x^2-6x+1)/((3x^2+6x+7)^2)

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derivative of

\frac{x + 1}{3 x ^{2} + 6 x + 7}

\frac{- 3 x ^{2} - 6 x + 1}{( 3 x ^{2} + 6 x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 1}{3 x ^{2} + 6 x + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 1 ) ( 3 x ^{2} + 6 x + 7 ) - \frac{d}{d x} ( 3 x ^{2} + 6 x + 7 ) ( x + 1 )}{( 3 x ^{2} + 6 x + 7 ) ^{2}}

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

\frac{d}{d x} (3 x^{2} + 6 x + 7) = 6 x + 6

= \frac{1 \cdot ( 3 x ^{2} + 6 x + 7 ) - ( 6 x + 6 ) ( x + 1 )}{( 3 x ^{2} + 6 x + 7 ) ^{2}}

Simplify

\frac{1 \cdot ( 3 x ^{2} + 6 x + 7 ) - ( 6 x + 6 ) ( x + 1 )}{( 3 x ^{2} + 6 x + 7 ) ^{2}} : \frac{- 3 x ^{2} - 6 x + 1}{( 3 x ^{2} + 6 x + 7 ) ^{2}}

= \frac{- 3 x ^{2} - 6 x + 1}{( 3 x ^{2} + 6 x + 7 ) ^{2}}

\int sin^{2} (wt) d t

arctan (4 x)

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

\frac{\partial}{\partial x} (l - c)

\int x (15 x + 4) d x

What is the derivative of (x+1)/(3x^2+6x+7) ?
The derivative of (x+1)/(3x^2+6x+7) is (-3x^2-6x+1)/((3x^2+6x+7)^2)
What is the first derivative of (x+1)/(3x^2+6x+7) ?
The first derivative of (x+1)/(3x^2+6x+7) is (-3x^2-6x+1)/((3x^2+6x+7)^2)