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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = lo g_{6} (2 x^{2} + 4), at x = 4

(- 1, - 5), (1, - 2)

e^{t} \cdot sin (2 t)

t \to 2 lim (sin (\frac{π}{4} t))

x \to 1 lim (\frac{x ^{2 n} - 2 x ^{n} + 1}{x ^{2 m} - 2 x ^{m} + 1})

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