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

The derivative of (x^2)/(2-x^2) is (4x)/((2-x^2)^2)

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

The first derivative of (x^2)/(2-x^2) is (4x)/((2-x^2)^2)

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derivative of

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

\frac{4 x}{( 2 - x ^{2} ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{2 x ( 2 - x ^{2} ) - ( - 2 x ) x ^{2}}{( 2 - x ^{2} ) ^{2}} : \frac{4 x}{( 2 - x ^{2} ) ^{2}}

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

\int x sin (- 1 x) d x

\int e^{- y} d y

\frac{d}{d x} (ln (3 x + 1))

x \to 0 lim (\frac{1 - 2 cos ( x ) + cos ( 2 x )}{x ^{2}})

d er i v a t i v e y = - \frac{2}{5} x - 3

What is the derivative of (x^2)/(2-x^2) ?
The derivative of (x^2)/(2-x^2) is (4x)/((2-x^2)^2)
What is the first derivative of (x^2)/(2-x^2) ?
The first derivative of (x^2)/(2-x^2) is (4x)/((2-x^2)^2)