What is the derivative of (1-2x/(6+x)) ?

The derivative of (1-2x/(6+x)) is -(13)/((6+x)^2)

What is the first derivative of (1-2x/(6+x)) ?

The first derivative of (1-2x/(6+x)) is -(13)/((6+x)^2)

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\frac{d}{d x} (\frac{1 - 2 x}{6 + x})

- \frac{13}{( 6 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 2 x}{6 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 2 x ) ( 6 + x ) - \frac{d}{d x} ( 6 + x ) ( 1 - 2 x )}{( 6 + x ) ^{2}}

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

\frac{d}{d x} (6 + x) = 1

= \frac{( - 2 ) ( 6 + x ) - 1 \cdot ( 1 - 2 x )}{( 6 + x ) ^{2}}

Simplify

\frac{( - 2 ) ( 6 + x ) - 1 \cdot ( 1 - 2 x )}{( 6 + x ) ^{2}} : - \frac{13}{( 6 + x ) ^{2}}

= - \frac{13}{( 6 + x ) ^{2}}

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\frac{d}{d x} (a x^{n})

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\int (8^{x} - sec^{2} (x)) d x

What is the derivative of (1-2x/(6+x)) ?
The derivative of (1-2x/(6+x)) is -(13)/((6+x)^2)
What is the first derivative of (1-2x/(6+x)) ?
The first derivative of (1-2x/(6+x)) is -(13)/((6+x)^2)