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Popular >

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

Solution

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

Solution

\frac{10}{( 1 - 3 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( 1 - 3 x ) - ( - 3 ) ( 3 + x )}{( 1 - 3 x ) ^{2}} : \frac{10}{( 1 - 3 x ) ^{2}}

= \frac{10}{( 1 - 3 x ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (3+x/(1-3x)) ?
The derivative of (3+x/(1-3x)) is (10)/((1-3x)^2)
What is the first derivative of (3+x/(1-3x)) ?
The first derivative of (3+x/(1-3x)) is (10)/((1-3x)^2)