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

The derivative of (2+x/(1-2x)) is 5/((1-2x)^2)

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

The first derivative of (2+x/(1-2x)) is 5/((1-2x)^2)

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

\frac{5}{( 1 - 2 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( 1 - 2 x ) - ( - 2 ) ( 2 + x )}{( 1 - 2 x ) ^{2}} : \frac{5}{( 1 - 2 x ) ^{2}}

= \frac{5}{( 1 - 2 x ) ^{2}}

x \to 0 + lim (ln (\frac{2}{x}))

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

\int \frac{x ^{3}}{9 + x ^{8}} d x

k = 1 \sum \infty 0. 5^{k} t

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

What is the derivative of (2+x/(1-2x)) ?
The derivative of (2+x/(1-2x)) is 5/((1-2x)^2)
What is the first derivative of (2+x/(1-2x)) ?
The first derivative of (2+x/(1-2x)) is 5/((1-2x)^2)