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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int x^{2} e^{- \frac{x}{4}} d x

\frac{d}{d x} (cos^{2} (8 x))

(5 x + 3)^{\frac{1}{5}}

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

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