What is the derivative of (2x+3/(5x+4)) ?

The derivative of (2x+3/(5x+4)) is -7/((5x+4)^2)

What is the first derivative of (2x+3/(5x+4)) ?

The first derivative of (2x+3/(5x+4)) is -7/((5x+4)^2)

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\frac{d}{d x} (\frac{2 x + 3}{5 x + 4})

- \frac{7}{( 5 x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 3}{5 x + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x + 3 ) ( 5 x + 4 ) - \frac{d}{d x} ( 5 x + 4 ) ( 2 x + 3 )}{( 5 x + 4 ) ^{2}}

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

\frac{d}{d x} (5 x + 4) = 5

= \frac{2 ( 5 x + 4 ) - 5 ( 2 x + 3 )}{( 5 x + 4 ) ^{2}}

Simplify

\frac{2 ( 5 x + 4 ) - 5 ( 2 x + 3 )}{( 5 x + 4 ) ^{2}} : - \frac{7}{( 5 x + 4 ) ^{2}}

= - \frac{7}{( 5 x + 4 ) ^{2}}

What is the derivative of (2x+3/(5x+4)) ?
The derivative of (2x+3/(5x+4)) is -7/((5x+4)^2)
What is the first derivative of (2x+3/(5x+4)) ?
The first derivative of (2x+3/(5x+4)) is -7/((5x+4)^2)