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

The derivative of-(2x+3/((x^2+3x+2)^2)) is -(2(-3x^2-9x-7))/((x^2+3x+2)^3)

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

The first derivative of-(2x+3/((x^2+3x+2)^2)) is -(2(-3x^2-9x-7))/((x^2+3x+2)^3)

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

- \frac{2 ( - 3 x ^{2} - 9 x - 7 )}{( x ^{2} + 3 x + 2 ) ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

- \frac{2 ( x ^{2} + 3 x + 2 ) ^{2} - 2 ( x ^{2} + 3 x + 2 ) ( 2 x + 3 ) ( 2 x + 3 )}{( ( x ^{2} + 3 x + 2 ) ^{2} ) ^{2}} : - \frac{2 ( - 3 x ^{2} - 9 x - 7 )}{( x ^{2} + 3 x + 2 ) ^{3}}

= - \frac{2 ( - 3 x ^{2} - 9 x - 7 )}{( x ^{2} + 3 x + 2 ) ^{3}}

x \to 3 lim (3 x - 7)

\frac{1}{x ^{7}}

x \to 0 + lim (e^{x} - (1 + x))

\frac{\partial}{\partial x} (x \cdot arccsc (\frac{x}{2}))

\int 5 x^{2} + 1 d x

What is the derivative of-(2x+3/((x^2+3x+2)^2)) ?
The derivative of-(2x+3/((x^2+3x+2)^2)) is -(2(-3x^2-9x-7))/((x^2+3x+2)^3)
What is the first derivative of-(2x+3/((x^2+3x+2)^2)) ?
The first derivative of-(2x+3/((x^2+3x+2)^2)) is -(2(-3x^2-9x-7))/((x^2+3x+2)^3)