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

The derivative of (-3x-2)/(2x^2+x+3) is (6x^2+8x-7)/((2x^2+x+3)^2)

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

The first derivative of (-3x-2)/(2x^2+x+3) is (6x^2+8x-7)/((2x^2+x+3)^2)

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derivative of

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

\frac{6 x ^{2} + 8 x - 7}{( 2 x ^{2} + x + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (2 x^{2} + x + 3) = 4 x + 1

= \frac{( - 3 ) ( 2 x ^{2} + x + 3 ) - ( 4 x + 1 ) ( - 3 x - 2 )}{( 2 x ^{2} + x + 3 ) ^{2}}

Simplify

\frac{( - 3 ) ( 2 x ^{2} + x + 3 ) - ( 4 x + 1 ) ( - 3 x - 2 )}{( 2 x ^{2} + x + 3 ) ^{2}} : \frac{6 x ^{2} + 8 x - 7}{( 2 x ^{2} + x + 3 ) ^{2}}

= \frac{6 x ^{2} + 8 x - 7}{( 2 x ^{2} + x + 3 ) ^{2}}

\frac{d}{d x} (\frac{e ^{x}}{x ^{3}})

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

y^{^{'}} = (x - 14)^{2}

y^{^{''}} + 324 y = sec (18 x), y (0) = 2, y^{^{'}} (0) = - 1

n = 3 \sum \infty \frac{3}{n ^{2} - 3 n + 2}

What is the derivative of (-3x-2)/(2x^2+x+3) ?
The derivative of (-3x-2)/(2x^2+x+3) is (6x^2+8x-7)/((2x^2+x+3)^2)
What is the first derivative of (-3x-2)/(2x^2+x+3) ?
The first derivative of (-3x-2)/(2x^2+x+3) is (6x^2+8x-7)/((2x^2+x+3)^2)