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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{( 9 - x ^{2} ) ^{\frac{3}{2}}} d x

\int_{0}^{2} x e^{- 5 x} d x

\int \frac{x + 5}{x ^{2} + 11 x + 18} d x

\int x y cos (z) d z

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

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