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Popular >

derivative of (2x+5/(3x-1))

Solution

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

Solution

- \frac{17}{( 3 x - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( 3 x - 1 ) - 3 ( 2 x + 5 )}{( 3 x - 1 ) ^{2}} : - \frac{17}{( 3 x - 1 ) ^{2}}

= - \frac{17}{( 3 x - 1 ) ^{2}}

Popular Examples

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x \to 3 lim (2 x + ∣ x + 3 ∣)

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\int \frac{8}{9} x^{\frac{8}{9}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (2x+5/(3x-1)) ?
The derivative of (2x+5/(3x-1)) is -(17)/((3x-1)^2)
What is the first derivative of (2x+5/(3x-1)) ?
The first derivative of (2x+5/(3x-1)) is -(17)/((3x-1)^2)