What is the derivative of (1-4x/(5+x)) ?

The derivative of (1-4x/(5+x)) is -(21)/((5+x)^2)

What is the first derivative of (1-4x/(5+x)) ?

The first derivative of (1-4x/(5+x)) is -(21)/((5+x)^2)

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\frac{d}{d x} (\frac{1 - 4 x}{5 + x})

- \frac{21}{( 5 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 4 x}{5 + 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 ) ( 5 + x ) - \frac{d}{d x} ( 5 + x ) ( 1 - 4 x )}{( 5 + x ) ^{2}}

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

\frac{d}{d x} (5 + x) = 1

= \frac{( - 4 ) ( 5 + x ) - 1 \cdot ( 1 - 4 x )}{( 5 + x ) ^{2}}

Simplify

\frac{( - 4 ) ( 5 + x ) - 1 \cdot ( 1 - 4 x )}{( 5 + x ) ^{2}} : - \frac{21}{( 5 + x ) ^{2}}

= - \frac{21}{( 5 + x ) ^{2}}

\frac{d}{d x} (3 x^{2} - 4 x + 6)

y \to - 3 lim (y)

\int - e^{- 2 y} d y

\frac{d y}{d x} = 2 x - 3 y, y (0) = \frac{1}{3}

\int \frac{x ^{3}}{16 x ^{2} + 256} d x

What is the derivative of (1-4x/(5+x)) ?
The derivative of (1-4x/(5+x)) is -(21)/((5+x)^2)
What is the first derivative of (1-4x/(5+x)) ?
The first derivative of (1-4x/(5+x)) is -(21)/((5+x)^2)