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

The derivative of (1-x/(2+x)) is -3/((2+x)^2)

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

The first derivative of (1-x/(2+x)) is -3/((2+x)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

\int (sec (x))^{3} d x

\frac{7 x}{2 ^{x}}

(- 8, - 4), (- 6, - 1)

y = \frac{4}{3} x + 2

What is the derivative of (1-x/(2+x)) ?
The derivative of (1-x/(2+x)) is -3/((2+x)^2)
What is the first derivative of (1-x/(2+x)) ?
The first derivative of (1-x/(2+x)) is -3/((2+x)^2)