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

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

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

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

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derivative of

f (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}}

x \to 2 lim (ln (x - 1))

\int cos^{7} (θ) sin (θ) d θ

\frac{1}{( 1 + x ) ^{3}}

ln (\frac{4 x + 3}{3 x - 5})

\int_{0}^{3} ∣ 2 x - 1 ∣ d x

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