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Popular >

derivative of ((1-x))/((x+2))

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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