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Popular >

derivative of x/(3x+5)

Solution

derivative of

\frac{x}{3 x + 5}

Solution

\frac{5}{( 3 x + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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