What is the derivative of (6-7x/(2+x)) ?

The derivative of (6-7x/(2+x)) is -(20)/((2+x)^2)

What is the first derivative of (6-7x/(2+x)) ?

The first derivative of (6-7x/(2+x)) is -(20)/((2+x)^2)

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\frac{d}{d x} (\frac{6 - 7 x}{2 + x})

- \frac{20}{( 2 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 - 7 x}{2 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 - 7 x ) ( 2 + x ) - \frac{d}{d x} ( 2 + x ) ( 6 - 7 x )}{( 2 + x ) ^{2}}

\frac{d}{d x} (6 - 7 x) = - 7

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

= \frac{( - 7 ) ( 2 + x ) - 1 \cdot ( 6 - 7 x )}{( 2 + x ) ^{2}}

Simplify

\frac{( - 7 ) ( 2 + x ) - 1 \cdot ( 6 - 7 x )}{( 2 + x ) ^{2}} : - \frac{20}{( 2 + x ) ^{2}}

= - \frac{20}{( 2 + x ) ^{2}}

x \to 6 - lim (\frac{x ^{6}}{x - 6})

5 x, 2 x^{2}

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\frac{\partial}{\partial x} (2 x^{4} y + 16 y^{3})

What is the derivative of (6-7x/(2+x)) ?
The derivative of (6-7x/(2+x)) is -(20)/((2+x)^2)
What is the first derivative of (6-7x/(2+x)) ?
The first derivative of (6-7x/(2+x)) is -(20)/((2+x)^2)