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

The derivative of (3x+5/(x^2-x)) is (-3x^2-10x+5)/((x^2-x)^2)

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

The first derivative of (3x+5/(x^2-x)) is (-3x^2-10x+5)/((x^2-x)^2)

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

\frac{- 3 x ^{2} - 10 x + 5}{( x ^{2} - x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

3 (x^{2} - x) - (2 x - 1) (3 x + 5) : - 3 x^{2} - 10 x + 5

= \frac{- 3 x ^{2} - 10 x + 5}{( x ^{2} - x ) ^{2}}

\int \frac{5}{x ln ( 6 x )} d x

\int_{0}^{3} x 16 - x^{2} d x

\int \frac{1}{x ^{2} x ^{2} - 3} d x

x \to 0 lim (- x ln (x) - x)

\int x \cdot x d x

What is the derivative of (3x+5/(x^2-x)) ?
The derivative of (3x+5/(x^2-x)) is (-3x^2-10x+5)/((x^2-x)^2)
What is the first derivative of (3x+5/(x^2-x)) ?
The first derivative of (3x+5/(x^2-x)) is (-3x^2-10x+5)/((x^2-x)^2)