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

The derivative of (3x+2/(x^2-5x+3)) is (-3x^2-4x+19)/((x^2-5x+3)^2)

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

The first derivative of (3x+2/(x^2-5x+3)) is (-3x^2-4x+19)/((x^2-5x+3)^2)

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

\frac{- 3 x ^{2} - 4 x + 19}{( x ^{2} - 5 x + 3 ) ^{2}}

Solution steps

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

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

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

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

Expand

3 (x^{2} - 5 x + 3) - (2 x - 5) (3 x + 2) : - 3 x^{2} - 4 x + 19

= \frac{- 3 x ^{2} - 4 x + 19}{( x ^{2} - 5 x + 3 ) ^{2}}

\frac{d}{d x} (cos ((8 x^{2} + 9)^{5}))

f (x) g (x)

2 x^{2} + x - 1

x \to - 6 lim (\frac{( x ^{2} - 36 )}{x + 6})

\int \frac{2 e ^{x}}{e ^{2 x} + 1} d x

What is the derivative of (3x+2/(x^2-5x+3)) ?
The derivative of (3x+2/(x^2-5x+3)) is (-3x^2-4x+19)/((x^2-5x+3)^2)
What is the first derivative of (3x+2/(x^2-5x+3)) ?
The first derivative of (3x+2/(x^2-5x+3)) is (-3x^2-4x+19)/((x^2-5x+3)^2)