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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

4 y d x - x y - 3 x d y = 0

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

\frac{d}{d x} (9 x^{8})

x^{2} - 9

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