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Popular >

derivative of (1-3x/(4+x))

Solution

\frac{d}{d x} (\frac{1 - 3 x}{4 + x})

Solution

- \frac{13}{( 4 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 3 x}{4 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 3 x ) ( 4 + x ) - \frac{d}{d x} ( 4 + x ) ( 1 - 3 x )}{( 4 + x ) ^{2}}

\frac{d}{d x} (1 - 3 x) = - 3

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

= \frac{( - 3 ) ( 4 + x ) - 1 \cdot ( 1 - 3 x )}{( 4 + x ) ^{2}}

Simplify

\frac{( - 3 ) ( 4 + x ) - 1 \cdot ( 1 - 3 x )}{( 4 + x ) ^{2}} : - \frac{13}{( 4 + x ) ^{2}}

= - \frac{13}{( 4 + x ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (1-3x/(4+x)) ?
The derivative of (1-3x/(4+x)) is -(13)/((4+x)^2)
What is the first derivative of (1-3x/(4+x)) ?
The first derivative of (1-3x/(4+x)) is -(13)/((4+x)^2)