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Popular >

derivative of ((1-3x))/(2+x)

Solution

derivative of

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

Solution

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

Solution steps

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

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

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

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

Simplify

\frac{( - 3 ) ( 2 + x ) - 1 \cdot ( 1 - 3 x )}{( 2 + x ) ^{2}} : - \frac{7}{( 2 + x ) ^{2}}

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ((1-3x))/(2+x) ?
The derivative of ((1-3x))/(2+x) is -7/((2+x)^2)
What is the first derivative of ((1-3x))/(2+x) ?
The first derivative of ((1-3x))/(2+x) is -7/((2+x)^2)