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Popular >

derivative of (3x+5/(1+x))

Solution

\frac{d}{d x} (\frac{3 x + 5}{1 + x})

Solution

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

Solution steps

\frac{d}{d x} (\frac{3 x + 5}{1 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 5 ) ( 1 + x ) - \frac{d}{d x} ( 1 + x ) ( 3 x + 5 )}{( 1 + x ) ^{2}}

\frac{d}{d x} (3 x + 5) = 3

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

= \frac{3 ( 1 + x ) - 1 \cdot ( 3 x + 5 )}{( 1 + x ) ^{2}}

Simplify

\frac{3 ( 1 + x ) - 1 \cdot ( 3 x + 5 )}{( 1 + x ) ^{2}} : - \frac{2}{( 1 + x ) ^{2}}

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3x+5/(1+x)) ?
The derivative of (3x+5/(1+x)) is -2/((1+x)^2)
What is the first derivative of (3x+5/(1+x)) ?
The first derivative of (3x+5/(1+x)) is -2/((1+x)^2)