What is the derivative of y=(2x-3)/(3x+1) ?

The derivative of y=(2x-3)/(3x+1) is (11)/((3x+1)^2)

What is the first derivative of y=(2x-3)/(3x+1) ?

The first derivative of y=(2x-3)/(3x+1) is (11)/((3x+1)^2)

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derivative of

y = \frac{2 x - 3}{3 x + 1}

\frac{11}{( 3 x + 1 ) ^{2}}

Solution steps

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

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

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

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

Expand

2 (3 x + 1) - 3 (2 x - 3) : 11

= \frac{11}{( 3 x + 1 ) ^{2}}

1 + 4 x

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

\int_{2}^{4} 5 t^{2} d t

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

\frac{d}{d x} (- 8 cos (- 4 x - 3))

What is the derivative of y=(2x-3)/(3x+1) ?
The derivative of y=(2x-3)/(3x+1) is (11)/((3x+1)^2)
What is the first derivative of y=(2x-3)/(3x+1) ?
The first derivative of y=(2x-3)/(3x+1) is (11)/((3x+1)^2)