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

The derivative of (3x-5/(2x+3)) is (19)/((2x+3)^2)

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

The first derivative of (3x-5/(2x+3)) is (19)/((2x+3)^2)

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

\frac{19}{( 2 x + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

3 (2 x + 3) - 2 (3 x - 5) : 19

= \frac{19}{( 2 x + 3 ) ^{2}}

x \to 0 lim ((sin (\frac{x}{2}))^{x})

\int \frac{x ^{2}}{x ^{3}} d x

\int 4^{t} d t

\frac{d}{d y} (x^{y})

\frac{\partial}{\partial x} (e^{x} + y^{2})

What is the derivative of (3x-5/(2x+3)) ?
The derivative of (3x-5/(2x+3)) is (19)/((2x+3)^2)
What is the first derivative of (3x-5/(2x+3)) ?
The first derivative of (3x-5/(2x+3)) is (19)/((2x+3)^2)