What is the derivative of (3x/(5x^2-2x-9)) ?

The derivative of (3x/(5x^2-2x-9)) is (3(-5x^2-9))/((5x^2-2x-9)^2)

What is the first derivative of (3x/(5x^2-2x-9)) ?

The first derivative of (3x/(5x^2-2x-9)) is (3(-5x^2-9))/((5x^2-2x-9)^2)

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\frac{d}{d x} (\frac{3 x}{5 x ^{2} - 2 x - 9})

\frac{3 ( - 5 x ^{2} - 9 )}{( 5 x ^{2} - 2 x - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{5 x ^{2} - 2 x - 9})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{x}{5 x ^{2} - 2 x - 9})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d x}{d x} ( 5 x ^{2} - 2 x - 9 ) - \frac{d}{d x} ( 5 x ^{2} - 2 x - 9 ) x}{( 5 x ^{2} - 2 x - 9 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (5 x^{2} - 2 x - 9) = 10 x - 2

= 3 \cdot \frac{1 \cdot ( 5 x ^{2} - 2 x - 9 ) - ( 10 x - 2 ) x}{( 5 x ^{2} - 2 x - 9 ) ^{2}}

Simplify

3 \cdot \frac{1 \cdot ( 5 x ^{2} - 2 x - 9 ) - ( 10 x - 2 ) x}{( 5 x ^{2} - 2 x - 9 ) ^{2}} : \frac{3 ( - 5 x ^{2} - 9 )}{( 5 x ^{2} - 2 x - 9 ) ^{2}}

= \frac{3 ( - 5 x ^{2} - 9 )}{( 5 x ^{2} - 2 x - 9 ) ^{2}}

What is the derivative of (3x/(5x^2-2x-9)) ?
The derivative of (3x/(5x^2-2x-9)) is (3(-5x^2-9))/((5x^2-2x-9)^2)
What is the first derivative of (3x/(5x^2-2x-9)) ?
The first derivative of (3x/(5x^2-2x-9)) is (3(-5x^2-9))/((5x^2-2x-9)^2)