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Popular >

derivative of y=(3x-1)/(6x+5)

Solution

derivative of

y = \frac{3 x - 1}{6 x + 5}

Solution

\frac{21}{( 6 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x - 1}{6 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x - 1 ) ( 6 x + 5 ) - \frac{d}{d x} ( 6 x + 5 ) ( 3 x - 1 )}{( 6 x + 5 ) ^{2}}

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

\frac{d}{d x} (6 x + 5) = 6

= \frac{3 ( 6 x + 5 ) - 6 ( 3 x - 1 )}{( 6 x + 5 ) ^{2}}

Expand

3 (6 x + 5) - 6 (3 x - 1) : 21

= \frac{21}{( 6 x + 5 ) ^{2}}

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integral of x/((4x+5)^2)

\int \frac{x}{( 4 x + 5 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(3x-1)/(6x+5) ?
The derivative of y=(3x-1)/(6x+5) is (21)/((6x+5)^2)
What is the first derivative of y=(3x-1)/(6x+5) ?
The first derivative of y=(3x-1)/(6x+5) is (21)/((6x+5)^2)