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

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

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

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

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

- \frac{11}{( x - 3 ) ^{2}}

Solution steps

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

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

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

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

Simplify

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

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

\int \frac{1}{2 x ^{2} - 16} d x

\int \frac{4 - x ^{2}}{x} d x

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

x \to - 4 lim ((x)^{2})

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

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