What is the derivative of (1-4x/(2+x)) ?

The derivative of (1-4x/(2+x)) is -9/((2+x)^2)

What is the first derivative of (1-4x/(2+x)) ?

The first derivative of (1-4x/(2+x)) is -9/((2+x)^2)

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\frac{d}{d x} (\frac{1 - 4 x}{2 + x})

- \frac{9}{( 2 + x ) ^{2}}

Solution steps

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

\frac{d}{d x} (1 - 4 x) = - 4

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

= \frac{( - 4 ) ( 2 + x ) - 1 \cdot ( 1 - 4 x )}{( 2 + x ) ^{2}}

Simplify

\frac{( - 4 ) ( 2 + x ) - 1 \cdot ( 1 - 4 x )}{( 2 + x ) ^{2}} : - \frac{9}{( 2 + x ) ^{2}}

= - \frac{9}{( 2 + x ) ^{2}}

\frac{d y}{d x}, x y = y^{3}

\int \frac{2 v}{2 - 3 v ^{2}} d v

x y^{2} - 5 y + 6

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

\int x e^{4 x} d x

What is the derivative of (1-4x/(2+x)) ?
The derivative of (1-4x/(2+x)) is -9/((2+x)^2)
What is the first derivative of (1-4x/(2+x)) ?
The first derivative of (1-4x/(2+x)) is -9/((2+x)^2)