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

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

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

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

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

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

Solution steps

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

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

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

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

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

Simplify

\frac{2 x ( 2 - x ) - ( - 1 ) x ^{2}}{( 2 - x ) ^{2}} : \frac{4 x - x ^{2}}{( 2 - x ) ^{2}}

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

x \to 0 lim (sin (x) ln (x))

\int \frac{29 x ^{2}}{x ^{2} - 4} d x

y = x^{2} + 2 x, y = x + 2

\int \frac{1}{8} t d t

y = tan (2 x)

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